This little corner gets The Six Counties, The North, Northern Ireland ( the "official" title, I believe), Ulster (irritating because of its inaccuracy), British-occupied Ireland, this sectarian statelet, our wee province and on and on.

I'll let someone else list the possibilities for the South.

As for the island as a whole try Joyce, "The old sow who eats her own farrow". Or….

"This lovely land that always sent
Its writers and artists to banishment
And in a spirit of Irish fun
Betrayed her leaders one by one
'Twas Irish humour wet and dry
Flung quicklime into Parnell's eye