Not sure is this is your James but looking on Rootsweb site for Des Moines cemeteries, I found the following:

http://www.rootsweb.ancestry.com/~iadesmoi/Toomstone/FlintRi...

Greenwood Cemetery
Flint River Twnshp, Burlington, IA

ROW 10

GRAHAM, JAMES A. 28 Mar 1836 – 10 Jan 1906

GRAHAM, MARY D. INGHRAM (maiden name) Wife 3 Oct 1845 – 15 May 1931

and then

ROW 24

GRAHAM, RACHAEL LEAH 22 Aug 1882 – 7 Mar 1968 (Brothers & Sisters)

GRAHAM, JAMES L. BURK 1 July 1865 – 20 Mar 1944 (Brothers & Sisters)

GRAHAM, ALEXIS GREEN 21 Oct 1867 – 27 Aug 1944 (Brothers & Sisters)

I know the maiden name for possible mother, Mary, was not correct and I wasn't sure if your James had the siblings listed. Thought it was worth a look.