http://en.wikipedia.org/wiki/Irish_nationality_law
Acquisition of citizenship
At birth
An Irish passport (Irish: pas Éireannach) may be issued to people holding Irish citizenship by the Department of Foreign Affairs
A person born on the island of Ireland on or after 1 January 2005:[3]
is automatically an Irish citizen if he or she is not entitled to the citizenship of any other country;[4]
or is entitled to be an Irish citizen if at least one of his or her parents is:
an Irish citizen (or someone entitled to be an Irish citizen);[5]
a British citizen;[6]
a resident of the island of Ireland who is entitled to reside in either the Republic or in Northern Ireland without any time limit on that residence;[7]
or
a legal resident of the island of Ireland for three out of the 4 years preceding the child's birth (although time spent as a student or as an asylum seeker does not count for this purpose).[8]