Irish naturalisation/citizenship

Cutting a long story short my i am from N.Ireland my husband is turkish.
He came to ireland via Dublin,He has lived in N.Ireland for 13 years his last Irish visa/stamp was in 2010 then he got an eea family member visa from the british embassey this is now expiring, as he never applied for permanent residency as we where originally told that because he was married to an eu national nobody can stop him entering when i am with him....So we where told wrong and now its coming back to haunt us. my question is can he apply for Irish naturalisation/citizenship or any of the Irish visas even though we live in the North of Ireland which technically is still living on the island of Ireland which is 1 of the requirements but does he need to have a recent gardai stamp or enrty visa to apply to the irish government...

From what you've posted, he has been living in Northern Ireland on an EEA Residence Permit since 2010-ish correct? It doesn't matter that he doesn't have a Garda stamp / irish via. Once he is living legally on the island of Ireland (i.e. the 32 counties), then he can apply for Irish citizenship (he is legal because of his EEA Residence Permit - the lack of a recent Garda stamp doesn't matter). But prepare for a long wait.

@spoonk

You are entitled to apply for an Irish Passport, yourself.

I would recommend you to apply for an Irish passport, then he can apply for an irish citizenship as a spouse of an irish citizen.