I research the Irish Family History Foundation's database. It contains 12,700,000 surviving rcds for abt 70% 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 30%.
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 Finan B 1885 +/- 1 yr, somewhere in Ireland, with the father's forename unknown, I found 4 rcds: 1885, 2-1886 (all Roscommon), and 1886 Co. Tipperary.
For Tho(mas) Finan B ????, somewhere in Ireland, with the father's forename unknown, I found 135 B rcds dating from 1796.
You will need an exact DOB, parent(s) name(s), and/or placename(s) to pick which, if any, rcds are for these ancestors. Suggest you inquire for her death cert. at the AZ Bureau of Vital Statistics or similarly named agency.
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.