According to one of legends of Oyama mountain (in Kanagawa) regarding the founding of Oyama-dera and Oyama Afuri Shrine:
“Two volumes of picture scroll made in 1532 and preserved by the Shrine tell us a legendary tale on how the Shrine was established. Once upon a time in the 7th century, there was a powerful and rich man named Tadatoki Someya (his date of birth and death unknown). He is the founder of Amanawa Jinja in Kamakura), controlling the area of today’s Kanagawa Prefecture. At age over 40, he was still childless. At one time, Tadatoki and his wife prayed to god so that they might be blessed with a child. Their wish was answered soon afterward, and they gave birth to a baby boy in 689. The couple raised him with tenderest care attaching a statuette of Kan’non Bosatsu (Avalokitesvara in Sanskrit) to his body as a guardian deity.
One day when the boy was two years old, a golden-colored eagle flew down to their home and the eagle snatched him away. All that happened in a split second while they could do nothing.. The eagle flew away to the west, some 500 kilometers to Nara near Todaiji, carrying the boy, and put him down on a cedar-tree branch. By quite a chance, a priest named Gi-en (?-728) of Todaiji passed under the tree. The eagle asked him to take care of the boy and left. (The tree is today called “Roben-cedar” and stands near the Nigatsu-do Hall adjacent to Todaiji.)
Tadatoki and his wife went almost insane with grief losing their only child. They started a long journey heading west in search of the missing boy. After more than decade of hardships, they finally came across the boy in Nara, when they visited Todaiji. The child turned out to be a high-ranking priest of Todaiji with the name of Roben (689-773). The couple were able to identify him since Priest Roben produced the statuette of Kan’non he had been attaching to his body. Reunion of the family encouraged them to come back to their home in Kanagawa, where Priest Roben erected the Oyama-dera, the origin of the today’s Shrine.”
Eagle-ancestor stories and eagle-shamanic myths:
In “Eagles carrying off babies and children“, the author of the article noted that birds carrying off children are common themes in shamanic myths:
“Shamanism and myth
Bob Rickard  notes a study of Japanese Shamanism, The Catalpa Bow by Carman Blacker which describes legends of children kidnapped by the tengu, mercurial beings, half hawks, half men, who haunt woods and mountain tops ( I note that in Norse myth Loki is associated with a hawk, as is Frey, and that in Egyptian mythology Horus has the head of a hawk). The tengu turn into golden eagles to carry off children who are reared inside hollow trees then returned to human society. Shamanic traditions (and some poltergeist cases) in a number of societies describe children vanishing to be found, high in a tree or an inaccessible place with no idea of where they are or how they got there. Another interesting twist is the name Svanhild, the swan being another large and potentially dangerous bird with mythological associations, though this is probably pure coincidence
Rickard also recounts another case, with links to shamanic traditions, where a child was carried off by an eagle but his body was never found. A few months later the father saw and shot the eagle and took the body home. The mother, who was pregnant, immediately went into labour from the shock of seeing the body. The child allegedly looked like an eagle and had two talents: rowing and singing.
It is worth noting also that in Arabia the Owl is a bird of ill omen, the embodiment of evil spirits that carries off children at night (and some owls are very big).
This note has almost exclusively been concerned with eagles carrying off children but other birds of prey have poked their beaks in. While individual reports of birds carrying off children should be treated with suspicion, especially older reports, there is nothing inherently improbable in an eagle carrying off a child up to around ten years old. In one case there is an interesting link to shamanic traditions, and while the idea of an eagle carrying someone, or their spirit, off may be an archetype, the archetype may have had a basis in reality and be an expression of ancient memories, just as the young of certain species of bird instinctively cower when they see the shadow of a paper cut out of a hawk. But that is speculation that needs to be fleshed out or refuted.”
The closest version to this Oyama-dera tale is the one recounted in the John Michell Mysteries, where Michell writes of the eagle clan whose ancestor was supposedly abducted as a baby but survived after having lived in an eyrie with the little eagles:
” Several old pubs are called The Eagle and Child. Their sign is an eagle standing over a swaddled baby. This is the crest of the Stanley family. As Earls of Derby they once ruled as kings in the Isle of Man. The source of their greatness was their ‘eagle ancestor’. He was abducted as a baby and lived in an eyrie with the little eagles.”
This raises the intriguing possibility there might even have been an ancient eagle clan peoples from the Caucasus region, from whom dispersed such eagle ancestor tales eastwards to Siberia (and possibly as far as Japan) as well as westwards through the Celtic migrations (identified as R1b haplotypes by Oppenheimer) perhaps. For example, the Scottish clan the Munros, have presiding over their crest an eagle, and the Clan Munro Association states that the Munros made the transition from Celtic chiefs to feudal lords.
Incidentally, the myth of Prometheus, who — in eternal punishment, has his liver eaten daily by an eagle, is chained to a rock in the Caucasus, — a link pointing to the same region where the Celtic warriors are now believed to have originated.
Good legends and bird fairytales abound, like the tales of storks bringing babies, and swan fairytales. But just how plausible is a story of an infant being carried away by an eagle?
I can begin by saying that a few years ago on the beach at Enoshima, I was extremely frightened by a surprise attack by a black kite (see videoclip) that swooped down and snatched a hamburger right out of my hand, just as I was about to lift it to my lips. Although the bird was not snatching “me”, it was extremely bold and aggressive, and not least afraid of an adult-sized person, who was not alone, to boot.
There are in fact known reports of children being carried off by eagles and of attempts by eagles … New York Times Jul 1, 1910 published a report entitled EAGLE TRIES TO STEAL CHILD.; But Finds Two-Year-Old Boy Too Heavy — Bird Dodges Mother’s Club, the incident took place in the rear backyard of their home.
Weekly World news Sept 4, 2011 – “Eagle flies away with two-year-old” reported a 2 year old boy having been snatched off from a playground near El Huecu, Argentina by an eagle, but that had been set down in its nest 4 miles away. The incident was documented by photographs because the boy’s father who is a photojournalist, allegedly happened to be taking photographs of his son in the playground at the time. The photos look somewhat photo-shopped to me, especially the second one where the stiff body position looked strange to me…
John Michell Mysteries writes that baby-snatching incidents by eagles were once common in Scotland and the Isles:
“An attempted ‘avian abduction’ was in the news recently. A three-year-old girl was playing on a beach in New Hampshire, when an American bald eagle swooped down and grabbed her with its talons. Her father chased the bird away and she escaped unharmed.
She was a lucky girl. Some children have been carried off by eagles, and then dropped from heights or eaten. But in some cases they have lived to tell the story. In 1977 MarIon Lowe, a boy of ten, was attacked by giant condors outside his home in Illinois. His parents and neighbours saw one of the birds carry him into the air. It dropped him when they yelled and waved. He was not hurt but so shocked that his hair grew white.
Baby-snatching by eagles was once quite common in Scotland and the Isles. The Nicholson family of Shetland are descended from a girl who, as a baby, was carried by a sea eagle to its nest on the island of Fetlar. It was under a ledge in a steep cliff-face. A boy, Robert Nicholson, was lowered to it on a swinging rope. He took the girl from among the eaglets and later married her. Scientists are suspicious of these stories. They claim that no bird can lift more than its own weight. A golden eagle weighing 8lb pounds could just about carry off a new-born baby. But even a 12lb condor could not take an older child. Yet in every part of the world, from ancient to modern times, there are records of children being snatched by eagles….“
Eagles carrying off children and babies has investigated this topic and given the reports some scrutiny:
“New York Times May 20th 1904 (citing the London Express of May 9th) stated that an eagle swooped down and carried off an 18 month old girl playing outside her fathers cottage about a mile from Invershin station on the Highland railway line. Her body was found, mutilated, in the crags where eagles nested. The article notes that two years earlier an eagle had killed and carried off a dear but that it had been fifty years since a tragedy like this had occurred. The eagle was never found. However this case has perhaps too many circumstantial details and was not reported locally 
Biofort  describes 30 cases of avian abduction mainly in the USA, and a few from Europe, some of which are summarised here here. In two separate cases a (different) bald headed eagle tried to carry off a two year old child: the second attempt succeeded. The first was foiled when some men working nearby tried to drive it off, but the eagle would not give up until someone shot at it. In two cases an eagle tried to snatch a 9 and a10 year old child respectively. In one case the eagle had an estimated wingspan of ten feet. Two eagles fought to the death over a 6 month old baby one had carried away. A local taxidermist in Ouakoke valley, near Wilkesbarre, Pa stuffed a giant bald headed eagle that had been killed when trying to carry off a three year old girl. A 70 year old woman weighing 160 pounds died after being attacked by an eagle that tried to carry her away. A five year old child was carried 50 yards by an eagle that was unable to get more than ten feet off the ground.
Of these cases only one involved an adult, all seem to have involved unusually large eagles and small ( that is lightweight) children. Many were foiled by nearby adults who either drove off the eagle or killed it. It is possible that the eagles mistook the children for their normal prey: in India tigers do not normally attack humans who are standing up but farm workers who are crouching down may be mistaken for deer and attacked. The workers carry a large hat on their back that holds a picture of a human face to prevent the tiger making a mistake.
Loren Coleman  notes that such reports were not uncommon in the 1920s and were also ridiculed by authorities who had not investigated the cases personally. The most recent case seems to have been in 1977 where a ten year old child was carried some 10 feet. Despite what skeptics say I would imagine some eagles could carry off a small child and the Philippine Eagle is also known as the Monkey Eating Eagle. It has a wingspan of around two metres: sometimes up to 8 feet, and weighs 6 to 9 kg. Its diet includes mostly flying lemurs, some squirrels, snakes, civet cats, hornbills, and occasionally bats and monkeys.
A case that seems to be well documented and investigated,  occurred in 1932 in Norway when three year old Svanhild Hartvigsen ( her married name) was carried away by an eagle and survived, living to a ripe old age but haunted by a fear of eagles….
The Scottish account given above by the New York Times is suspect not only as a secondhand citation from a LONDON paper (400 miles away) but for the lack of such details and possibly too many heart wrenching details like the feathers in the babies hand. Also there seems to be no account of the attack in any local papers.
Another point to bear in mind, they say is that the eagle may have been attacking the child, who may have come too close to the eagle’s nest. Most of the reports seem to indicate the victim was nowhere near the nest.
A final point is skepticism about how much an eagle can lift and carry. One expert commented that eagles can carry only about 5 pounds. However the 1977 case in Lawndale Illinois involved a ten year old boy. The case was investigated by Loren Coleman who interviewed the mother. (And the author of the skeptical blog above admits he can make nothing of this case). There is also a recent case of a deer being found on a power line ,  and the same site shows golden eagles carrying deer long distances and attacking bears. Furthermore the now extinct Haast’s eagle , which hunted the giant flightless mao in New Zealand seems to have been incredibly strong. The possibility of a relict of Haast’s eagle in the USA while unlikely cannot be ruled out, nor can the possibility of a small population of native American giant eagles with extraordinary strength. It would be worthwhile plotting the occurrence of these abduction stories to see if they defined a geographical area.”