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 Eliza Barrett B 1851 +/- 2 yrs, Co. Kilkenny, with a father forenamed Mich(ael), I found 1 rcd in 1851, St. John's RC parish.
For Ann Barrett B 1850 +/- 4 yrs with the father's forename unknown, I found 36 rcds with 0 in Kilkenny. This infers Ann was a cousin and came from a different county.
For John Carroll B 1849 +/- 4 yrs somewhere in Ireland with a father forenamed John, I found 49 rcds.
For Ju(dith) Ronan M 1847 +/- 4 yrs somewhere in Ireland, I found 2 rcds in 1843, Co. Kilkenny, both in St. John's RC parish. These may be duplicates.
For Michael Barrett M ditto, I found 1 rcd in 1843, St. John's RC parish. This is a match. The rcds are highly likely to be for your ancestors - no guarantee. A view of the detailed M rcds SHOULD show they married each other. If so, then the rcds MAY list their parents' names and other info.
For John Carroll M 1847 +/- 4 yrs somewhere in Ireland, I found 348 rcds - too many to list here, but 1 of which was in St. John's parish, Co. Kilkenny, and 1 in Glenmore parish, 1847, also Kilkenny
For Mary Kirby M ditto, I found 54 rcds with 9 in Kilkenny, but none in St. John's parish. However, 1 is in Glenmore in 1847. This and John's rcd have a good chance of being for your ancestors. Again, a view will reveal all info on the rcd and validate/invalidate it.
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.