Martha C Stone in the following family is a likely match for your Caroline Stone. Note the name of the father, Washington. Caroline probably named her son Washington Griffin after her father. Washington Stone's first wife had died before the 1850 census. Accoridng to Nash Co, NC marriage records her name was Nancy J Edwards.
1850 United States Federal Census Nash, North Carolina Washington Stone 49m farmer $900r NC Elizabeth R Stone 18f NC W G W Stone 20m farmer NC Benja F Stone 17m farmer NC Martha C Stone 11f NC Sarah A Stone 8f NC Louisa L Stone 7f NC
North Carolina Marriage Bonds, 1741-1868 Groom: Washington Stone Bride: Nancy J Edwards Bond Date: 12 Oct 1829 Bond #: 000086776 County: Nash Record #: 01 113 Bondsman: William H Edwar Witness: Benja H Blount
I just found information on this family on Rootsweb's World Connect. It says that Marha C's name was Martha Caroline.