Hi Carolyn,
It is Union Hill Cemetery on Fairfield Drive in Myrtle Grove, Florida. A suburb of Pensacola. I have a list of the burials and the only Clayton I see is a Pearlie Clayton, 1873-1938.
Our Genealogy Society has tried to document all of the cemeteries in the county. We had most of them on the website on USGenWeb but there was some mess going on with that site so it's moved to a rootsweb address. I've got to look for the new site. We have many other cemeteries with CSA burials. I sort of just did Union Hill because it's where so many of my family are. You may find it if you google West Florida Genealogical Society or WFGS on rootsweb.

Pam