There is some information in the Virginia Historical Society that mentions a Cosby family.
The Peter Cottrell listed is the son of William and Susan (Halsey) Cottrell of Henrico Co., VA who married Mary M. Cosby.
Peter and Mary M. died before 1880 in Kentucky. They had a daughter named Lillie V. Cottrell that married William Henry Harrison.
There is information listed on the Harrison family.
I don't know what amount of information is on Cosby family but it is listed.
Item# 33 Personal Name Cottrell family. Title Bible records, 1830-1909 Phys. Descript.  leaves : handwritten ; 11 x 8 1/2 in. Call Number Mss6:4 C8295:1 General Note Photocopy made from the original Bible in the possession of Paul Frank Meyers, Phoenix, Ariz., in 1983. Summary Note Concern the family of Peter Cottrell (1830-1878), as well as the Cosby and Harrison families. Provenance Note Photocopied through the courtesy of James H. Harding, Richmond, Va., 30 October 1985. Subject (Name) Cottrell family -- Genealogy. Subject (Name) Cottrell, Peter, 1830-1878 -- Family. Subject (Name) Cosby family -- Genealogy. Subject (Name) Harrison family -- Genealogy. Ind. Term-Genre Bible records. Subject Location of original: Meyers, Paul Frank. Subject Source: Harding, James H. Personal Name Cottrell, Peter, 1830-1878.