what would be the genitive form of Nua Geirseí? Nua Geirseá?

No, not really. It's rather hard making a genitive of non-Irish words, and Geirseí is no more Irish than Jersey. (Which by the way is a Norse name, so none of the two is English either...). The number of Irish nouns ending in "í" in the singular is very low indeed. Still, there are such words. Something you won't find is the combination of "e+í", it is alien to Irish. (It should be "Geirsí) And even if the spelling were acceptabel, Geirseí (as pronounced by an Irish speaker) would not sound particularly like Jersey.

I must admit that I'm somewhat reluctant to invent new names for places. It another thing with places that already do have an Irish name, but an invented name do not make them more Irish. I've never felt the need to change my name from Jonas nor my city from Helsinki/Helsingfors when I speak Irish. If a different thing with English names, though. Most of them do have a corresponding Irish forms and in those cases I fully understand that one would want to use the Irish versions.

Two more points about the name "Nua Geirseí". It is bad Irish to place the adjective before the noun. Some few adjectvis do come before the nound they qualify. "Sean"=old is one of them, "nua" is not. I am fully aware of the fact that New York is called Nua Eabhrac in Irish and I do use it myself when speaking Irish. Still, it is not good Irish and those who coined it could have done better.

All points above are of course just my own opinions but there is one very real reason why you might want to awoid using the name "Nua Geirsí". For anyone speaking Irish it can just mean one thing, it sounds like a bad pronunciation of geirí, meaning "fatter". "Geir" is the Irish word for "fat". You might want to avoid that label ;-)

Slán go fóill,
Jonas