I search the IFHF's online database at 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 almost non-existant. Many B/M/D events either weren't recorded, or haven't survived.
For a John Ward and Elizabeth ? marriage in 1804 +/- 5 yrs, Co. Meath, I found 1 record in 1804. Thanks for having decent data. This MAY be for your ancestors. A view (usually at a small fee) of the detailed record MAY show their parents' names and other info. At this early date record keeping was sloppy with many ommissions.