Ooh, ooh, I know this one!
^((Although only in terms of the early English/British empire c. 16th-17th century.))
To answer this question, we first need to understand that race in terms of "black" or "white" were not so clear-cut at the time of Ireland's colonisation by the English under Elizabeth I. Many accounts by English merchant traders reveal that religion and home country was more important in determining friend from foe in the increasingly far-reaching world of international trade. While skin tone was a factor in determining these two important aspects of a stranger, it was merely a means of discerning religion or home country. We see this in the 1608 journal of John Jourdain who stopped a Pemba ship en route to Zanzibar:
"Covert says that ‘sixe or eight were pale and white, much differing from the colour of the Moores; yet being asked what they were, they said they were Moores, and shewed us their backes all written with characters; and when we affirmed them to bee Portugals, they then told us the Portugals were not circumcised."
As we see here, skin tone is like circumcision in being a means of identification, not necessarily an inherently derogative thing. So to ask whether the British saw the Irish as "black" is to apply a relatively modern concept of race and racism to an historical context preceding it.
This is not to say that the English didn't persecute the Irish for their origins. Indeed, Ireland is where England really cut its teeth in becoming an imperial coloniser and as such narratives were created to justify aggressive colonisation of Ireland. Such justifications included:
Let's break these down.
Religious differences
England had just gone through a turbulent Reformation, bouncing back and forth between being either Catholic or Protestant and persecuting the other before settling on Protestantism under Elizabeth I. The Reformation never reached Ireland which, despite Norman invasions in the 12th century, had been long left to its own devices since then and continued to practice an early form of Catholicism. The English Crown has very limited control or influence over the "Old English" Lords from the Norman invasion. This is grounds for Just War.
Cultural inferiority
As mentioned, the lands of Ireland were largely ruled by "Old English" Lords. The English viewed the Irish as barbarous savages (although this was a term used to anyone you disagreed with at this time, even your next-door neighbour - not explicitly race-related). As such, they used the "Old English" as an example of how integrating with a primitive culture i.e. nomadism, can lead to a reversion of civilisation. This nomadism played into a notion of Natural Law where if a land isn't used to its full potential, another sovereign Christian prince is entitled to settle those lands. Similar logic was used in settling North America a little later. In practice, if the land is not being used in the same way as the English i.e. intensive farming, logging, cities etc., then it's a free-for-all. Ireland is referred to as a wasteland and, so, is justifiable for colonisation by English forces.
Overpopulation in England
London's population had exploded in the mid 1500s and so the streets were full of starving, diseased layabouts and the country was full of too many little lords and not enough land to parcel out. So, to kill two birds with one stone, Elizabeth divided up Ireland into parcels of land for plantations and sent off young lords with hordes of poor cannon fodder. As such, there was a strong push factor for settling Ireland as well as pull factors.
All in all, Ireland and the Irish were subject to the first great act of English "othering". In order to justify the brutal occupation of their lands, texts were written by such "great writers" as Edmund Spenser (The Faerie Queene) depicting the Irish as a brutal, uncivilised people who ate their own babies. While some proto-racial arguments were also employed such as associating them with the Scythian warrior tribes from Classical mainland Europe (a tenuous link given they were historically up in the Ural mountains), but it could not be equated to being "black" in slave era America. It was well before such overarching theories were developed as a result of the Transatlantic Slave Trade.
For an example of how Irish and other poor whites of Europe got wrapped up in ideas of eugenics in the early USA, I recommend watching Gangs of New York. It really shows how races were being perceived in the mid-1800s, not just in America but by Europeans too. Hope this helps!