Joseph B. Renfro was a son of Joseph B. Renfro and Margaret McCarty. He and Martha had six children I know of: James, Margaret Melvina, Cyrus, Lucinda, and Eveline.
James B. (Sr.) was a son of James William Rentfrow and Lydia (Harris?). James William was a son of William (b1702) and Elizabeth Cheney. From there back it's shaky, but he may go back to Symon Renfro who arrived in Jamestown from Scotland in 1638.