In modern times Black people in Ireland have been present in small numbers since the mid-16th century. Mainly concentrated in the major cities, especially Dublin, many in the 18th century were owned by wealthy families. There were other Afrikans in Ireland who were not slaves, notably Olauda Ikwuano, who visited Belfast once from London, but wrote and self-published best selling accounts of his experience of slavery.
In the 1800s, many people believed that Irish people who had dark complexions were somehow related to Afrikans. In 1862, John Beddoe, an esteemed ethnologist, published Races of Britain, in which he described people of Celtic descent as having features similar to those of Afrikan descent. The term "Black Irish" might have been derived from this viewpoint. Of course Western racism with its anti-Afrikanism and negative attitude towards black things including human beings, made being a Black Irish a thing of distaste and people considered inferior to white Irish. Could the descendants of these Blacks have given us the term "Black Irish"?
The term "Black Irish" has also been applied to the descendants of Irish emigrants who settled in the West Indies. It was also used in Ireland by Catholics in Ulster Province as a derogatory term to describe the Protestant Planters.
What is the origin of the term? One notion is that black hair is evidence of Spaniards marooned in Ireland following the wreck of the Armada. But the number of shipwrecked Spanish sailors who remained in Ireland for any length of time was small and insignificant.
It has also been 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. Staying with this ancient Black Irish connection, perhaps the Black Irish were the vestiges 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 linguistic evidence of pre-Gaelic settlement. We assume they were descendants of Grimaldi, the first human habitation in Europe. Who were the Grimaldi? Grimaldi were Afrikan migrants, who were short, burnt of skin and wooly hair. Sounds like Herodotus describing the ancient Egyptians or Kemeyu.
The story of St Patrick is one of Christianity's victory over Celtic traditional religion, which was a form of religious expression that retain many Afrikan elements. Why do I say Afrikan elements, for two reasons: we know their religious practices contained Nature worship; there existed many deities that were communicated with through rituals; the use of sacrifice was fundamental, animal and supposedly human; they believed that the soul survived death; reverence for the sun; and they believed in reincarnation. (Often the Celtic religion is refereed to as Druidism, named after their priesthood and religious leaders.) And all these ideas can be found in traditional Afrikan spirituality. You say, well, they can be found in the spiritual beliefs of other people as well, and I would agree. However, we know that the Afrikan phenotypes were still present, perhaps even dominant, among the early Celts because the Greek historian Ephorus of Cyme (c. 405 BCE) reports that the Celts were Blacks or Ethiopians, and the Roman senator and historian Tacitus wrote in 80 AD, that many of the Celts and Picts were as dark as Ethiopians. It is interesting that Ephorus and Tacitus writing nearly 500 years apart both describe the Celts as Ethiopians. Now this is not what we envision when we thinks of the Red-haired white-skinned Irish. But both linguistic and genetics supports the claims of these two ancient writers.