I research the Irish Family History Foundation's database. It contains 12,700,000 surviving rcds for abt 72% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Co Donegal rcds were added to this database July 7, 2009.
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).
I can't find B/M rcds for Peter McAvey/McAvoy or Lillian Palmer/Polvier anywhere in Ireland within a relevant range of dates.
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.