I searched the Irish Family History online database at ROOTSIRELAND.IE. It has abt 20M B/M/D records for most Irish counties. Records before 1863 are increasingly sparse: almost non-existant before 1800. Protestant records are the least likely to have survived.
For a Andrew Phillips and Bri(gid) Behan marriage 1859 +/- 5 yrs, somewhere in Ireland, with the parents' names unknown, I found 0 records.
For Andrew Phillips B 1835 +/- 5 yrs, ditto, I found ditto.