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 available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome), and the National Library of Ireland on microfilm.
For Cat(herine) Hickey M 1881 +/- 4 yrs, somewhere in Ireland, I found 16 rcds - too many to easily summarize here, but NONE in Co. Kildare. You may want to expand the search range.
For Mic(hael) Morrissey M ditto, I found 11 rcds - again too many, with only 1, 1877, in Kildare.
For Cat(herine) Hickey B 1860 +/- 2 yrs, Castledermott, Co. Kildare, with the father's forename unknown, I found 1 rcd, 1860. Father's forename was Andrew.
For Andrew Hickey M 1856 +/- 4 yrs, Castledermott, Co. Kildare, I found 1 rcd, 1859. A view of the detailed rcd SHOULD reveal both the bride's name and parents' names.
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.