Irish legend says that the Tuatha de Danann (the people of the Goddess Danu) are the fairy folk; the fairies, pixies and brownies who inhabit the mounds, or Sidhe, of the Irish countryside. But upon closer examination, one discovers that the Tuatha de Dannan were actually a people who inhabited Ireland in times long past.
According to the Annals of the Four Masters, the Tuatha de Danann ruled Ireland from 1897 BC to 1700 BC. The story of their invasion of Ireland and subsequent war with the Fir Bolg (the previous inhabitants) is a fascinating chronicle of ancient Irish history.
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The wildest notion is that black hair is evidence of Spaniards marooned in Ireland following the wreck of the Armada. As we've had occasion to discuss in the past, the number of shipwrecked Spanish sailors who remained in Ireland for any length of time was trivial.
I have also heard it said the black Irish were the first settlers of Ireland--maybe the Phoenicians. The red Irish, meanwhile, were descendants of the Normans, and the blond Irish are descended from the Vikings. One of many drawbacks to this theory is that it seems to leave the Gaels completely out of the picture.
A more plausible but still essentially unprovable take on this idea is that black hair is a vestige of an indigenous population of short dark-haired types overrun by the fair-haired Gaels. Supposedly there are more black Irish in the western part of the country, which fewer Gaelic invaders reached.
There is archaeological and, I'm told, linguistic evidence of pre-Gaelic settlement. But how it was concluded that they were short and black-haired I do not know. Seems like a silly thing to make a fuss over in any case
Other writers say it relates to "Tribe of Dan". Some of the early Tribe of Dan bailed out of Egypt (along with some of the Tribes of Judah and Asher) when things were getting hot there for Abrahams descendents. This is before those 12 Tribes left for Palestine about 1415 BC. These "early leavers" traveled to and set up colonies in Spain and Ireland.
These early Danites should also not be confused with the major travels of the Tribe of Dan later, after which are named the Danube River, and the Dneiper and others, and after which the nation Denmark is named. The Danites were key in the peopleing of all of Scandinavia.
Also, the book of Jeremia discusses in some detail the later travel of the Prophet Jeremia, eventually ending up in what is believed to be Ireland. (Land of "jerries",etc. .)" It's a long story.
(Note: I'm no expert on Irish history, but was interested enough to spend a Post-Doctoral summer at Trinity College Dublin a few years ago, studying Ancient Irish History.)