Conrad Mawyer (Moyer/Moirer) was part of the family of Jacob Mawyer (Mayer) who was included in the 1785 Albermarle Co. VA. census. The census list Jacob Mayer as "head of household of 11 white souls". While I have not been able to find all of the 11 people I have found that the number includes Jacob and his wife Frances and the children Conrad, Margaret (Peggy), Leonard, Catherine, and Sarah. Jacob had a brother also living in the area (Batesville, Covesville, North Garden) that may be included.
The family migrated from PA. to Albermarle Co. VA. somewhere between 1774 and 1785. Conrad's brother Leonard died in 1855 at 81 years of age. His death certifcate states that he was born in PA. It seems that Conrad was older that Leonard which means that Conrad was also born in PA.
Conrad Mawyer married Elizabeth Lankford in Oct. 1806. She had a brother Charles S. Lankford who married Elizabeth Farrar in Feb. 1802 in Amherst Co. The father of Elizabeth and Charles S. Lankford was William Lankford.
I have been working on the Mawyer family history for many years but I have not been able to establish were Conrad and his family went. He disappears from all Albermarle, Nelson and Amherst county records. My best guess is that they migrated through the Roanoke Valley into Tennessee. This seems likely because many families in this area at this time were making this move including many of the Lankford family.
I hope this helps. If there are any other question around the Mawyer family that you think I may be able to help you answer please feel free to ask.