Bobby,
Just to add a little more to what Tom and Gary have already provided, my personal research of the Compiled Service Records on the 50th Georgia Infantry Regiment shows a James J. Stone enlisting in the Coffee Guards (Company C) at Douglas (Coffee County), Georgia on 3/4/1862. He was wounded on 7/2 at Gettysburg and shown as AWOl on the 2/65 Muster Roll. His pension records say he was home on sick furlough, which could have very well been true. He was paroled at Thomasville, Georgia on 5/17/65.
There was also a William Stone in Company C. He enlisted on 3/4/62. Maybe he was a relative of James. William was captured at Leesburg, Va in 9/62 and paroled a month later. Was also wounded in the head at Chancellorsville on 5/3/63 and Cold Harbor on 6/3/64. He was paroled at Lynchburg, Va on 4/13/65.
Three other Stones were in the 50th, but may not have been related to James. They were: George R. of Co A (Pierce County), killed at Fox's Gap 9/14/62; John W. of Co G (Clinch County), captured at Ft Loudon, Tn 11/29/63 and later took oath of allegiance and joined the US Navy in 1/64; and William H. of Co A, wounded/captured at Fox's Gap 9/14/62, wounded/captured at Gettysburg, captured at Cedar Creek 10/19/64 and paroled at Point Lookout, Md 6/19/65. He filed for a Confederate Service Pension in Baker County, Fl in 1907.
Just a long shot, but you may want to contact the regional library in Douglas, Georgia. I believe they have a genealogy section and someone may be able to see if they have anything else on file that could help with your research.