For all of the birth or marriage dates after 1863, you are in luck. B/M/D registration was civil after this date and comprehensive. Civil rcds are at the General Register Office. Contact it at http://www.groireland.iehttp://www.groireland.ie for B/M/D certificate copies. Fees apply
For dates B4 1864, I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
1/2 of Co. Cork rcds aren't in the database yet. Suggest you wait until they are. The short-term alternative is to visit an LDS Family History Center/Library and search its microfilm copies of parish registers.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.