He was probably born in what is now Ohio County, WV.
According to the records from West Alexander Cemetery (which can be seen in the Wheeling Room at the Ohio County Library in Wheeling, WV), James Curtis Atkinson was buried in Plot #F-25, which is the same plot as his son, George Andrew Atkinson. There is no stone, though. The "empty" space in the picture here, next to the flat black marker for G. A. & L. May (McDaid) Atkinson is probably the location of the graves of James C. and his wife, Sarah Jane (Kimmins) Atkinson.
He was a son of George & Susannah (Faris) Atkinson. He and his wife were the parents of 7 children. Two who died as infants, and Eva Ida Jane Giles, George Andrew Atkinson, Allen Kimmons Atkinson, Elizabeth May Grandstaff, and William Jay Alexander Atkinson.