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 Chr(istopher) Carroll B 1807 +/- 4 yrs, Co. Louth, with the father's forename unknown, I found 1 rcd in Togher RC parish. The father's forename was rcd'd as "Tom."
For B(ridget) Carroll B ????, Togher parish, Co. Louth with a father forenamed T(homas), I found 1 rcd in 1805.
For Ja(mes) Carroll B ditto, I found 2 rcds: 1798, and 1802.
For Mat(hew) Carroll B ditto, I found 1 rcd in 1804.
For Cat(herine) Carroll B ditto, I found 3 rcds within a relevant range: 1798, 1810, and 1811.
For Ju(dith) Carroll B ditto, I found 2 rcds with a relevant range: 1811, and 1818.
For Owen Carroll B ditto, I found 2 rcds within a relevant range: 1799 and 1812.
For Th(omas) Carroll M 1800 +/- 4 yrs in Co. Louth, I found 7 rcds: 1797, 1798, 3-1799, 1801, and 1803. 3 of the 7 rcds are in Togher parish. A view of the detailed rcds MAY show that only 1 has Cat(herine) as the mother's forename.
Some of the above are highly likely to be for your ancestors. Where there are several possibilities, the mother's forename should permit you to pick which, if any, is the correct rcd.
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.