According to the info found at this site, your John E. Cooley was a member of Company K (the Jasper Guards), 37th. Miss. Infantry Regiment.

http://mscgr.homestead.com/MSCGRcolh.html

A capsule history of the 37th. Regiment is available at this site.

http://mississippiscv.org/MS_Units/37th_MS_Inf.htm

John E. Cooley's residence is noted as Jasper County in his service records which is where John & Mary were living in the 1860 census, his age is not noted in his service records.

Military service records for John E. Cooley can be ordered from this site http://history-sites.com/research/index.html and thanks to Jim Huffman's research neither John or Mary applied for a Confederate Soldier/Widow's pension.