I think you would need to kick England very hard. But it could be done.
I say out upon Irish settlement of *Canada! Let them come across it, sure, and set up an outpost or so, but give me a Hibernian South America any day over that (blame @DanMcCollum ). Chalk it up to my standing contempt for keeping non-Iberian European settlers confined to the temperate zones.
EDIT: In all seriousness, I can see a Gaelic *Canada being relatively simple to do with the right series of events. And should a unified, navally-inclined Eire (necessary for the OP in general) wish for their own place in the tropical goods market, there's always the smaller Caribees or Jamaica.
You know, I never DID confirm Gaelic South America in my Amalingian timeline. Though the irony of having the Irish colonize Brazil and call it ... Brazil would be pretty good
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I shan't say anything further on the matter, but I'm sure you know my stance on such things
In all seriousness, while I don't at all hold to the determinist notion that things like access to currents and relative location in Iberia is a prerequisite for a Western colonial power, I will admit that it does help. That being said, if there's any nation outside of Portugal/Spain in kick-starting a westward/long-distance colonial and exploratory fleet (with the right shipwrighting and at-home stability established that is), it's Eire.
I think you would need to kick England very hard. But it could be done.