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 Cunningham, the earliest M rcd in Co. Meath is for 1823.
For Margaret Hogg, the earliest M rcd in Co. Meath is for 1859.
For Cunningham DOBs 1818-1838 with a father named James, there are 15 B rcds. Some of these MAY be for the children of James and Margaret. A view of the detailed rcds SHOULD show the parents' names. This will validate/invalidate the rcds.
It appears the M events weren't rcd'd, rcds didn't survive, or haven't been digitized yet (slim chance).
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.