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 James McGarrity M 1795 +/- 4 yrs somewhere in Ireland, I found 7 rcds: 1791 Westmeath, 1793 Louth, 1795 Dublin, 1795 Westmeath, 1797 Sligo, 1798 Dublin, and 1798 Longford.
For Elizabeth Pettigrew M ditto, I found 0 rcds.
Will leave it to you to screen the database for their offspring. Some DOB would help greatly.
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.