Not quite. Only Irish Citizens can apply for Irish passports; the question is how to achieve that.Â
Under the terms of the Good Friday Agreement, UK Citizens who were born in Northern Ireland are entitled to claim Irish Citizenship and thus can apply for an Irish passport.  Applicants under this method do not need to have qualified under residency, so they don't have to have ever lived there to qualify.
Non-Irish citizens living in Ireland can claim Irish nationality after 5 years of residency ().
Under the agreement, all UK citizens have the right to live, work and vote in Ireland and vice versa for Irish citizens, once they have lived in either country for 5 years, they can apply for Irish/British nationality and thus be entitled to apply for the relevant passport. Residence means they have to have actually live there for the time required, you cannot go and live there for a while, then go back home to wherever you came from, then 5 years later apply for a passport.
How to apply for an Irish passport is described on the Irish Government .
This is the reason why Ireland has never signed up to Schengen.
