If the purpose of this inquiry is to determine the specific site and identity of a grave, I fear there will be disappointment even if records for Tyner's Station are ever located. That information almost never appears in CSA medical registers or related papers, and graves were usually given temporary markers. After the war these were sometimes collected for use as firewood.
Another approach to this problem would be to identify the actual site of the hospital and nearby burial sites. You would then learn if any graves at Tyner's Station were marked, or if the site still exists. Someone in the Chattanooga area will probably have this information and be happy to help.