Lynn,
"Leofric, I haven't found the birth on IGI pedigree files for Robert Weldon Tarleton 1748, another one to recheck ! "
Sorry - wrong year! should've been 1750. To find it, and many more submitted by a woman in British Columbia, click on Advanced search, Pedigree File, then just enter the surname Tarleton, and Ireland, but with no dates and you'll see them all.
There is also on the Ancestral File of IGI a George Matcham Tarleton by a submitter from Texas, but he has the birth in Kent, not Ireland.