I research the Irish Family History Foundation's database. It contains 12,800,000 surviving rcds for abt 70% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Cos. Donegal and Derry were recently added to the database.
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).
Note 4 - Microfilms of parish church rcds are kept by the National Library of Ireland (NLI).
For Mary O'Gara M 1863 +/- 2 yrs, Co. Roscommon, I found 2 rcds, 1860 and 1863, Tibohine-Fairymount RC parish.
For Tho(mas) Carty M ditto, I found 1 rcd in 1863, Tibohine-Fairymount RC parish. This is an apparent match. These are HIGHLY likely to be for your ancestors. A view of the detailed rcds LIKELY will show they married each other. If so, then the view MAY show their parents' names as well as other lesser info. This is useful in identifying and validating earlier B/M rcds.
For Tho(mas) Carty B 1838 +/- 4 yrs, Co. Roscommon, I found 9 rcds, none in Tibohine-Fairymount RC parish.
For Mary O'Gara B 1841 +/- 4 yrs, Co. Roscommon, with a father forenamed Tho(mas), I found 2 rcds: 1844 and 1837. Both were in Tibohine-Fairymount RC parish.
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.