I search the IFHF's online database @ ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Records before 1863 are increasingly sparse. By 1800, they are nearly non-existant.
For James O'Connor B 1807 +/- 5 yrs, somewhere in Ireland, with the parents' names unknown, I found 133 records of which 4 are in Co. Wexford. You will need some idea of his parents' names (assuming these were recorded) to pick which, if any, is the right one.