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 sparse.
For Peter McEvoy B 1865 +/- 4 yrs in all Ireland, I found 13 B rcds. For Co. Meath, I found 1 B rcd in 1864. This MAY be for your ancestor. B registration was civil after 1863. The civil rcds are kept by the General Register Office. This office's website is http://www.groireland.iehttp://www.groireland.ie.
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.