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 county, 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).
For Mich(ael) Corrigan B 1825 +/- 2 yrs somewhere in Ireland with the father's forename unknown, I found 15 rcds: 1823 TIP, 1823 LOU, 3-1823 MEA, 1825 KIL, 1825 LOU, 1825 ROS, 1826 TIP, 1826 KIL, 2-1826 LNG, 1827 ANT, 1827 LNG, and 1827 LOU.
The actual "Irish Free State" was created during the fight for Irish independence ca 1916 to 1922. However, this name was used before its creation as a symbol of aspiration.
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.