Ohio didn't start to record births until 1867 so that option is out.
I'd look in FamilySearch or the Ohio Archives for their marriage license to see if their parents are on it. If not, then I'd look for their newspaper marriage announcement.
I'd also look at the Ross County Archives, www.rossprobatejuvenile.com/Archives.htm
for his father's probate records.
The Ross County Ohio Genealogical Society, www.rootsweb.ancestry.com/~ohrcgs/
has resources too. Successful Searching!