I know what you're on about, I'm from Ireland myself. The Spanish Armada theory was disproved a while back as there weren't enough survivors from the wreckage to leave a significant enough mark on the local gene-pool. As you say the most likely theory is a recurring phenotype from Northern Iberia, where the Goidelic and Brythonic Celts likely originated.
Another theory is that the swarthy complexion is a remnant of the island's pre-Aryan population, who as far as we know had dark tan to olive skin, and not the Bantu black that the UK National History Museum gave Cheddar Man in that shameless propaganda piece, as they were likely descended from proto-Semites that migrated into Europe from Anatolia.
Funny enough, and to get my autism post back on topic, she actually pointed to the 'black Irish' as having meant they were literally black people, and not just a relatively darker complexion.