Hi,
There is a volunteer in Franklin County who will look up death notices/obits. His parents names might be in his death notice. You'll find the volunteer's contact info at
www.gengathering.com.
If that doesn't work out, you can contact your local public library and ask them to locate the applicable newspaper on microfilm via inter-library transfer. Then you can look for his death notice but be sure to look carefully throughout the newspaper because during that time frame they interspersed them throughout a newspaper.
Another option is to contact the Frank County Genealogical & Historical Society,
www.fcghs-oh.org/. Successful Searching!