Corkley is a townland in either the parish of Keady, or Armagh.
I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840. Rare B4 1800.
For James Kirkwood B 1860 +/- 4 yrs in Co. Armagh, I found 0 B rcds. The closest is in 1875. His father was not named Samuel. This date is probably too late for your timeline.
Expanding the search to all Ireland, I get similar results.
The Kirkwood surname seems Scots-Irish. B/M/D registration for protestants was civil after abt 1856. Suggest you contact the Public Record Office for Norther Ireland for its rcds: google PRONI to lead you to its database.
Google the Foundation's name to lead you to this database. Pls post your search results to this genforum msg.