Charles is correct in that a few years after the war, the Federal Government set up a program to relocate known soldier’s graves to a National Cemetery. Those doing the work did the best they could to identify the remains, but they usually just had wooden markers that had rotted and few, if any, personal items in the grave. Sadly, a lot of these soldiers are buried as UNKNOWNS.
On March 7, 1868, 323 soldiers buried at the Rolla cemetery were relocated to Jefferson Barracks National Cemetery (St. Louis, MO). At least 77 of these soldiers are listed as UNKNOWN.
I looked through my listings for Jefferson Barracks National Cemetery and I could not find a Charles Monroe Cunningham.
To do some searching yourself, see the message thread, this board: “Looking for a Veteran’s Grave Site?” on January 11, 2007 and you will find a couple of on-line search locations.