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 Cat(herine) and Mary Cadden 1855-1862, Co. Leitrim, with the father's forename unknown, I found 2 rcds: Catherine B 1857, Mary B 1860. For Catherine's 1857 rcd, the father is forenamed Pat(rick). For Mary's 1860 rcd, the name is Henry. This conundrum infers that either, or neither, rcd is for your ancestors. Rcd transcription for Leitrim is essentially complete - this county's database is complete. Doubtful if any more rcds will be added.
There is a slim chance that some rcds didn't survive to be transcribed, but were captured by earlier efforts. These repose in parish record microfilms created by the LDS and the National Library of Ireland. The LDS efforts started in the 1940s, the NLI rcds in 1922. The LDS Family History Library can help you access what it has.
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.