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 and almost non-existant before 1800. Many B/M/D events either weren't recorded, or the records haven't survived.
For Robert Wark B 1790 +/- 20 yrs, somewhere in Ireland, with the parents' names unknown (this is a very broad search), I found 0 records.