I search the IFHF's online database at ROOTSIRELAND.IE. It has abt 20 M church, civil, census, etc for MOST Irish counties. Records before 1863 are increasingly sparse and almost non-existant before 1800.
For Ed(ward) McNamee B 1857 +/- 3 yrs, somewhere in Ireland, Co. Tyrone, with the parents' forenames unknown, I found 1 record in 1854. The parents' forenames for this record are James and Sally.
For an Ed(ward) McNamee and Ann Quinn marriage, somewhere in Ireland, with no other information, I found 0 records. It appears this event either wasn't recorded, or the record hasn't survived. There is a SLIM chance that it hasn't been transcribed yet.
For Ed(ward) McNamee B 1830 +/- 5 yrs, somewhere in Ireland, with the parents' names unknown, I found 2 records: 1835 Co. Louth, and 1828 Co. Offaly.
For Ann Quinn B 1830 (exact), ditto, I found 22 records - far too many to easily explore.