I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds B4 1840 are increasingly sparse, B4 1800 rare. I only search the existing database.
For Richard Andrew/s B ???? in Armagh, I didn't find any B rcds in the database. There is 1 B rcd for Richard Andrews in 1833 Louth. The next closest were 1829 Cork and 1844 Dublin.
For Moses Andrew/s B ???? in all Ireland, there is 1 B rcd of indeterminate year in Co. Down.
Google the Foundation's name to lead you to this database. Pls post your search results to my genforum msg.