http://www.ohiohistory.org/dindex/results.cfmThere are several Paul Thomas listed in the OH Historical Society on line index. In particular, Paul Thomas, d. 3/13/1926 Vol 4996 Certificate 18347. Of these choices, this individual died in Mahoning County. Alliance is in Stark Country, but we are right on the border with Mahoning, and if your ancestor lived out of town, this could be him. If it is, it will probably have the place of burial listed too.
There is no dedicated Veteran's Cemetery in Alliance, but veterans are buried in all of the local cemeteries. They include: Alliance City Cemetery, Highland Memorial Cemetery, St. Joseph's Cemetery, as well as several smaller township cemeteries on the edges of town.
I've had really good luck with the Stark Country Library. They hold microfilm death certificates. You could also check with Rodman Public Library in Alliance. I would think someone in Reference could look up any cemetery listings for you.
http://www.starklibrary.org/genealogyservices.htmlhttp://www.rodmanlibrary.com/My first recommendation would be the Stark County Library. Those gals are great and very willing to help. We have construction at the city library at the moment and things are spread all over. Have you tried census records? Try Stark, Mahoning, Columbiana counties.