Roster of Confederate Soldiers, 1861-1865, shows 3 JAMES STONE's:

Stone, James GA 14th Inf. Co.C
Stone, James GA 39th Inf. Co.C
Stone, James GA 50th Inf. Co.C

The 14th GA Inf was in the ANV as part of Hapton's-Anderson's-Thomas' Brigades from November 1861 to April 1865, Yorktown to Appomattox. James is the only STONE listed in the 14th GA Inf.

The 39th GA Inf was Army of TN. James is the only STONE listed in the 39th GA Inf.

The 50th GA Inf was also ANV from July 1862 to April 1865 serving in Drayton's-Semme's-Bryan's-Simms' Brigade, from 2nd Bull Run to Appomattox. Besides James, there is:
Stone, George R. GA 50th Inf. Co.A
Stone, John W. GA 50th Inf. Co.G
Stone, William GA 50th Inf. Co.C
Stone, William H. GA 50th Inf. Co.A

Stone, Wesley GA 56th Inf. Co.G - the only STONE listed in this unit

Stone, David A. AL 28th Inf. Co.K
Stone, Francis M. AL 28th Inf. Co.C
Stone, T.A. AL 28th Inf. Co.C
Stone, William P. AL 28th Inf. Co.C
Stone, William R. AL 28th Inf. Co.K

The Roster shows JAMES STONE in the following Alabama units:

Stone, James AL 25th Inf. Co.H
Stone, James AL 26th Cav. Co.C
Stone, James AL 42nd Inf. Co.G
Stone, James AL 62nd Inf. Co.H

The 25th AL Inf served with the Army of MS from Feb 1862 to November 1862, then Army of TN from November 1862 to April 1865

The 26th AL Cav I have no information on and might have failed organization

The 42nd AL Inf was part of the Army of West TN from September 1862 to January 1863; Dept of MS and East LA from January 1863 to July 1863; Army of TN from November 1863 to April 1865

The 62nd AL Inf was part of the Dept of AL, MS and East LA from March to May 1865

Based on what I found, I would suggest checking out the 14th and 50th GA Inf units.

Good hunting.