This is the only Cunningham listed for the 6th Missouri:

Charles William Cunningham, Private, Company C, 6th Missouri Infantry, enlisted March 25, 1861 at Van Buren, Ark. by Col. Clark for 3 years, detailed as Teamster February 9, 1863, captured at Vicksburg, Miss. July 4, 1863, paroled July 7, 1863, recorded, in hospital, sick, on the May/June, 1864 muster roll, 4 companies were consolidated with 6 companies of the 2nd Missouri, to be known as the 2nd & 6th Missouri Regiment October 1, 1863, wounded at Franklin, Tenn. November 30, 1864, captured at Blakeley, Ala. April 9, 1865, received at Ship Island, Miss., April 15, 1865, transferred to Vicksburg, Miss. May 1, 1865, surrendered and paroled at Jackson, Miss. May 12, 1865, swore allegiance to the United States, May 22, 1865 at St. Louis, dark complexion, light hair, blue eyes, 6’ _”, description on enlistment, 21 year old Farmer, born in Howard County, Missouri, resident of Boons Lick, Howard Co., Mo.

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Missouri