Rob, I have found two men that possibly could be your Ancestor depending which side he fought on these men were the only two that showed up on the Ancestry Civil War site by this name:You searched for J.S. Cunningham
[All U.S. Civil War Soldiers, 1861-1865 Results]

U.S. Civil War Soldiers, 1861-1865
about John S. Cunningham
Name: John S. Cunningham
Side: Union
Regiment State/Origin: Missouri
Regiment Name: 1 Missouri Engineers
Regiment Name Expanded: 1st Regiment, Missouri Engineers
COMPANY: H,D
Rank In: First Lieutenant
Rank In Expanded: First Lieutenant
Rank Out: First Lieutenant
Rank Out Expanded: First Lieutenant
Film Number: M390 roll 10

Source Information:
National Park Service. U.S. Civil War Soldiers, 1861-1865 [database on-line]. Provo, UT, USA: The Generations Network, Inc., 2007. Original data: National Park Service, Civil War Soldiers and Sailors System, online <http://www.itd.nps.gov/cwss/>, acquired 2007.
[U.S. Civil War Soldiers, 1861-1865]
about J.S. Cunningham
Name: J.S. Cunningham
Side: Confederate
Regiment State/Origin: Tennesee
Regiment Name: 1 Tennessee Cavalry.
Regiment Name Expanded: 1st Regiment, Tennessee Cavalry
COMPANY: D
Rank In: Private
Rank In Expanded: Private
Rank Out: Private
Rank Out Expanded: Private
Film Number: M231 roll 11
*** The second J.S. Cunningham, from Tennessee has also got a Pension record. His name was JAMES and his wife was a Catharine J. this was issued on Aug. 20th 1889. For more on this man go to this link:http://www.tngenweb.org/civilwar/csacav/index.html
Regards Patricia