You know, I've got kinda wacky - but fun - idea.
What if: So, following the Irish revolt against the rule of Elizabeth you saw the Flight of the Earls where major Gaelic rulers in Ulster fled their lands and made it to the continent to enter into military or governmental service with major Catholic powers such as France or Spain. What if, one of them gets a great idea: he approaches some of his continental friends with the plans of financing an colony of Irish ex-patriots in North America. The idea is simple: the colony will be nominally independent, but could certainly act as a counter-force to British interests in North America.
The initial wave of Irish is small, as to be expected, but a few small villages are constructed. Place, obviously, is very important here. I'm guessing that anywhere south of Virginia is going to be far too close to English colonies for comfort. New Amsterdam is likewise out and, north of that you get into the New England colonies. Unless we go with Georgia - likely too open to attack from the royal navy - this probably leaves Maine which had a much smaller English presence at the time. Maine also has the benefit of being close to New France who they look to as an obvious ally. This is meant to be a settler colony but also to turn a profit and so *New Ireland quickly becomes engaged in the fur trade and fishing (farming as well, but that's less likely to turn a profit).
Although the initial population is small, New Ireland begins to draw more Irish to its shores and the birth rate in this settler colony is high with new communities springing up. Eventually, realizing that they will need one another to defend against the English, Native Americans (and even encroachment by their allies) the different communities bind together to form a federation of sorts. Each town will send a representative to a common council which will oversee defense and trade negotiations. You have the beginnings of a Confederation of New Ireland.
Whether they go on to be conquered by the English during an alt-French and Indian War or maintain their position (maybe spreading over into Newfoundland at an early date) if open to others.
Like I said, kinda hair-brained idea - but is struck my suddenly and I kinda like it
