Given the probable mother shown in the censuses you give on his profile, Elizabeth Owens born abt 1824 in South Carolina. It is possible that she is Elizabeth Garner Owens, born 04 Feb 1823, died 25 Oct 1888, buried in the Garner family cemetery in Gray Court, Laurens, South Carolina https://www.familysearch.org/ark:/61903/1:1:QV29-15V8 Though I can't find a record for an Elizabeth Garner marrying someone surnamed Owens.
Joseph's family is suggested in a genealogy http://www.billputman.com/the-genealogy/putnam-putman-families/the-southern-putnam-putman-family/south-carolina/SCWilliam2.pdf as:
PURCHASE PUTMAN born June 11, 1847 in Laurens County and died there May 11, 1918. She married Joseph Harrison Owens about 1875. He was born October 5, 1851 and died in Laurens County July 6, 1894. They had: Perry Herbert Owens born November 17, 1878 in Youns, Lauren County and died in Laurens, Laurens County March 10, 1933. His wife was Bertha, born about 1883. They had two children Irene and Guy. Ethel Owens born in 1882 and died in 1917 all in Laurens County. She married Fed Thomas Hughes about 1900. He was born in October 1880 and died in 1912 all in Laurens County. They had three children: Wayne born in 1901, Joseph Chestley born in 1905 and Jessie born in 1908. Milum Oswell Owens born January 13, 1884 and died in Darlington, South Carolina in December 1880. He married Jessie Estelle Hammett. She was born in Georgia in September 1888 and died in Charleston, South Carolina December 1, 1953. They had two sons Millum and Joseph