Paula,
Since you have so little information on your ancestor's Civil War service I recommend you contact:
Missouri State Archives
State Information Center
P.O. Box 1747
Jefferson City, MO 65102
phone: 573-751-3280
Fax: 573-526-7333
E-mail: archref@sosmail.state.mo.us
or http://mosl.sos.state.mo.us/rec-man/arch.html
and perhaps also Arkansas State Archives and see if they can find a military service record for Jonathan Cunningham. You could also obtain forms from your local library to contact NARA in Wash. D. C. but I would think they would need to have more information than you now have to proceed with a similar request. Both Rolla and Springfield were major Union bases throughout the Civil War, and even knowing at which one Cunningham entered Union service gives little help.
Bruce Nichols