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 Fahey B 1827 +/- 4 yrs somewhere in Ireland with the father's forename unknown, I found 43 rcds - too many to summarize here.
For Marg(aret) Elliot B 1831 ditto, I found 11 rcds: 1827 Louth, 1827 Leitrim, 1828 Limerick, 1831 Louth, 1832 Kilkenny, 1832 Cork, 1832 Leitrim, 1832 Cavan, 1833 Dublin, 1834 Kildare, and 1835 Meath.
You will need an exact DOB, parent(s) name(s), and/or placename to pick which, if any, of these rcds are for your ancestors. Suggest you dig deeply into the St. Patrick's RC church rcds for their marriage rcd. This will likely give their ages, parents' names, and sometimes placename(s).
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.