A person can acquire Irish citizenship through the following method
Born on the island of Ireland
Everyone born on the island of Ireland before 1st January 2005 is automatically entitled to citizenship. After this date, to qualify for citizenship by birth one or more of the parents must be an Irish citizen at the time of the birth of the child, or have a legal right of residence in the State for three of the four years prior to the birth of the child.
You can qualify for citizenship by descent if you were born outside Ireland and your parents or grandparents are Irish citizens, once your grandparents were born in Ireland.
People born outside Ireland who fulfill the residency requirements for time spent legally living in Ireland can apply for citizenship. Applications generally take 6 to 12 months.
If you do not want to acquire Irish citizenship you but have lived in Ireland for over 8 years, you may qualify for permission to remain without condition as to time (Stamp 5). Naturalized Irish citizens with dual nationality who are required to travel on a non-Irish passport may apply for a Without Condition Endorsement (Stamp 6) as needed.
Descent of Irish Family
Through Legal residence in the State
Long Term Residency Stamp 5 and 6