If you have not got Irish born parents of grandparents it is still possible to become an Irish citizen. (See this page if you have an Irish grandparent)
You can marry an Irish Citizen:-
To claim Irish citizenship by marriage, you must meet the following conditions: · You must be married to an Irish citizen for at least 3 years · You must have had a period of one year’s continuous “reckonable residence” in the island of Ireland immediately before the date of your application · You must have been living on the island of Ireland for at least 2 of the 4 years before that year of continuous residence · Your marriage must be recognised as valid under Irish law · You and your spouse must be living together as husband and wife · You must be of good character and intend to continue to live on the island of Ireland · You must have made a declaration of fidelity to the nation and loyalty to the State. Certain periods of residence do not count for this purpose, for example periods when you did not have permission to remain in Ireland, or you were here on a student visa, or you were seeking asylum.
See this page about getting permission to remain in Ireland
You can also claim Irish Citizenship – from living in Ireland long enough. (Naturalisation or Naturalization)
If you wish to become an Irish citizen through naturalisation, you must:
· Be 18 years or older (you must be married if you are under the age of 18) or a minor born in the State after 1 January 2005
You must be of of good character – the Garda Síochána (Ireland’s national police) will be asked to provide a report about your background.
You must have had a period of one year’s continuous “reckonable residence” in Ireland immediately before the date of your application for naturalisation and, during the eight years preceding that, have had a total reckonable residence in Ireland amounting to four years.
You must Intend in good faith to continue to reside in the State after naturalisation You will also need to make a declaration of fidelity to the nation and loyalty to the State.
See this page about getting permission to remain in Ireland
Citizenship Section (Naturalisation) Irish Naturalisation and Immigration Service 13/14 Burgh Quay Dublin 2 Tel (within Ireland): LoCall 1890 551 500 (helpline available 10:00 a.m.-12:30 p.m. Tuesdays and Thursdays only Tel (from outside Ireland): +353 1 616 7700 (helpline available 10:00 a.m.-12:30 p.m. Tuesdays and Thursdays only E-mail: citizenship_mail@justice.ie