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).
For Thomas Paul Ryan B 1894 (exact), Emly CP, Co. Tipperary, with a father forenamed Thomas, I found 1 rcd.
For Bri(dget) Fitzgibbon M 1889 +/- 4 yrs somewhere in Ireland, I found 7 rcds: 1885 Cork, 2-1885 Limerick, 3-1890 Limerick, and 1892 Limerick.
For John Ryan M ditto, in Cork/Limerick, I found 58 rcds - too many to summarize here. There are POTENTIAL matches in Co. Limerick in 1885, 1890, and 1892 Limerick. Will leave it to you to screen these at the parish level to see if there are matches there. If so, one of the matches is likely to be for these ancestors.
For Bridget Fitzgibbon B ????, Charleville, Co. Cork, with the father's forename unknown, I found 1 rcd in 1845. This seems too early for your timeline.
For John Ryan B 1868 +/- 4 yrs, Cloughjordan, Co. Tipperary, with the father's forename unknown, I found 4 rcds: 1864, 1866, 1867, and 1869.
Some of the above MAY be for your ancestors. You will need exact DOB/DOM, parent(s) name(s), and or more placename(s) to pick which, if any, are the right ones.
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.