I have found the record of a Thomas Carroll born 14 Sept 1761 in Philadelphia, Pennsylvania. He is son of Thomas Carrell/Carroll Jr. and his wife Eleanor. Thomas Carroll Jr. is the son of Thomas Carroll and Mary Carroll's whose tombstone memorial is: Find A Grave Memorial# 10404910 I believe this family came from Northern Ireland.
U.S., Presbyterian Church Records, 1701-1970
Name: Thomas Carroll
Event Type: Baptism
Birth Date: 14 Sep 1761 Philadelphia, Pennsylvania
Baptism Date: 10 Oct 1761
Baptism Place: Philadelphia, Pennsylvania, USA
Church: First Presbyterian Church
Father: Thomas Carroll
Mother: Eleanor Carroll
Baptism just 10 days before his father's death
After Thomas's father died his mother remarried John Hart and their family migrated to Washington County and Allegheny County, Pennsylvania. John Hart's family records can be found in First Moon, Beaver, Pennsylvania by 1800. He has land warrents in Washington County, as well as Allegheny County. Most likely Thomas Carroll's son was with them. Eleanor Carroll Hart married John Hart 19 December 1763 in Philadelphia. His name is noted in the Probate Courts for Thomas Carroll's property's after his death. The record notes: Eleanor Hart wife of John Hart and widow of Thomas Carrell/Carroll. Thomas was a "Plasterer" in Philadelphia and owned land in 1757 on Spruce Street close to second street close to the Delaware River in Philadelphia.