Trying to say "The capital of Northern Ireland is Belfast".

I believe that is : Is é Beal Feirste an príomhchathair Tuaiscirt Éireann.

Since this involves the copula and the genitive, I'm not betting on myself having that right. And I'm pretty sure I left out a fada somewhere.
But then again, I might have actually said "Belfast is the capital of Northern Ireland".

Help??

Is é Béal Feirste príomhchathair Thuisceart Éireann.

- no article with príomhchathair because Tuisceart Éireann follows (a definite noun phrase)
- no genitive form of Tuisceart because Éireann follows (a definite noun)
- lenition of Tuisceart because it is definite.



There's no difference.
Béal Feirste as a proper name always comes first. Only intonation and context may help to differ:

Cad é príomhchathair Thuisceart Éireann? - Is é Béal Feirste príomhchathair Thuisceart Éireann. (B.F. as predicate)
Cad é an rud é Béal Feirste? - Is é Béal Feirste príomhchathair Thuisceart Éireann. (B.F. as subject)


If you change the order (i.e.: Is í p.T.É (ná) B.F.) the sentence rather means: "What the capital of N.I. is, is: Belfast"

Excellent explanation!