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 Mary Tieney B 1865 +/- 4 yrs somewhere in Ireland with a father forenamed James, I found 8 rcds: 1863 Leitrim, 1866 Mayo, 1867 Leitrim, 2-1868 Antrim, 2-1869 Tyrone, and 1869 Roscommon. None of these match for the birth yr. This implies either the rcd didn't survive, or hasn't been digitized yet. Suggest you wait until the database is more complete.
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.