Something Maverick posted has just reminded me how important a role Irish exiles often played in Spain and Spanish America in the 18th century after the Flight of the Wild Geese - everything from colonial administrators (Ambrosio O'Higgins) to nationalist rebels (his son Bernardo) to freakin' Prime Ministers (Richard Wall).
So while they ended up with a fair number of Irish (especially aristocrats) all throughout the Spanish Empire, I'm wondering if there could be established an actual dedicated Irish colony within the Spanish Empire. This might require a larger population from across society to successfully flee the island, but I don't think it's too far beyond the bounds of plausibility.
If it was in North America, you might even get a case where Irish people fake Protestantism to be allowed to settle in the Thirteen Colonies and then secretly follow an established route to the Spanish Irish colony instead.
So where might this colony be established? Given general policy in this era, I'm guessing it would be on a dodgy frontier somewhere, where Spain wanted to extend its power but didn't want to put its own colonists at risk (as Britain did with German refugee settlers in the Appalachians...)