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 John CREAN M 1857 (exact), Co. Leitrim, I found 1 rcd, Kiltoghert RC parish.
For Mary Murray M ditto, ditto. A view of the M rcds SHOULD show their parents' names as well as other info. However, if these names weren't on the original parish register, they are unlikely to be in this database either.
For Mary Murray B 1836 +/- 4 yrs, Kiltoghert RC parish, Co. Leitrim, with the father's forename unknown, I found 2 rcds: 1833, and 1837. Father's respective forenames were Farrell and Thomas.
For John CREAN B 1834 ditto, I found 0 rcds.
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.