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 Anastatia Reidy M 1855, somewhere in Ireland, I found NO rcds within a relevant range.
For Mary Reidy B 1862 +/- 1 yr, Co. Limerick, with a father forenamed Pat(rick), I found 1 1862 rcd, Co. Limerick, Dromcolliher RC parish.
For Mar(y) Dermody M 1856 +/- 1, somewhere in Ireland, I found 6 rcds: 1855 Kilkenny, 1855 Galway, 1856 Limerick, 1857 Tipperary, 1857 Kilkenny, and 1857 Longford.
For Pat(rick) Reidy M ditto, I found 1 rcd: 1855 Tipperary. This is a NO match with the rcds for Mary.
For Dermody siblings B 1837 +/- 4 yrs, somewhere in Ireland, with a father forenamed Kieran, I found Michael B 1833, Co. Kilkenny.
For Anastatia Dermody B 1835 +/- 4 yrs, Co. Kilkenny, with a father forenamed Kieran, I found 1 rcd, 1832, Freshford RC parish.
For Mar(ia) Dermody B 1831 ditto, I found 1 rcd, 1831, St. Canice's RC parish.
For Mary Cody M 1827 +/- 4 yrs, Co. Kilkenny, I found 25 rcds, with 2 in 1828, but none in Freshford RC parish.
For Kieran Dermody M ditto, I found 1 1828 rcd, Co. Kilkenny, Freshford RC parish. Either this is a NO match, or there was a transcription error.
For Kieran Dermody B 1805 +/- 4 yrs, somewhere in Ireland, with the father's forename unknown, I found 0 rcds.
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.
Hope this helps. Good luck.