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 Peter Tierney M 1846 (exact), Lackagh parish, Co. Galway, I found 1 rcd.
For Cat(herine) O'Brien M ditto, I found ditto.
The above are HIGHLY likely to be for your ancestors. A view of the detailed M rcds SHOULD reveal their parents' names and other info.
For Sarah Tierney B 1851 +/- 4 yrs in Co. Galway with a father forenamed Peter, I found 1 rcd in Donaghpatrick RC parish.
For POTENTIAL siblings B in Donaghpatrick with a father forenamed Peter, I found Mary 1852, and NO others. This is unusual in highly fecund Ireland. I found several other forenames within a relevant range in different parishes.
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.