There is a Quaker death record for William Greer born abt. 1769 who died in Milton, Ireland on May 21, 1841. But Wm's dad was probably in Adams County when Wm was born in 1797.

In 1810, Nathan, Finley, and William McGreer all lived in Tyrone.
Have you looked at all the church records for Tyrone for the birth of Wm? Also check the land records to see if Wm's father deeded land to him.