The surname Cluny/Cluney must have died out in Taghmon parish not long after Patrick left. A search on the subscription site Roots Ireland did not show any Cluny/Cluney baptismal records in Taghmon. There were a few Cluny/Cluney baptismal records in other parishes with the last baptismal record in 1869. By the 1911 census there were no Cluny/Cluney individuals in all of Co. Wexford.
You may want to consider a DNA test to see if you have matches with individuals who have Cluny/Cluney connections.