Death of Samuel Coulter in Wayne County, Ohio
Per the record below, a "Saml Coulter", born in Pennsylvania in 1796, died in Pike Station, Wayne Ohio in 1873. This could be William Kerr Coulter's father.
"Ohio Deaths and Burials, 1854-1997," database, FamilySearch(https://familysearch.org/ark:/61903/1:1:F6C1-C3N : accessed 4 December 2015), Saml Coulter, 20 Jan 1873; citing Pike Station, Wayne, Ohio, reference v 1 p 37; FHL microfilm 1,765,214.
Samuel Coulter buys 160 acres in Wayne County, Ohio
Samuel Coulter bought 160 acres in Section SE13 of Washington Twp, Holmes County, Ohio. Source: Early Land Records of Wayne County Ohio, page 183. Accessed 4/16/16 at Ohio History Center.
1850 census showing Samuel and Jane Coulter in Canaan Twp, OH
The census lists the following household members: Samuel (54); Jane (69); Elizabeth (21); Samuel (20); William (?); Robert B. (2). Samuel and Jane were born in PA, the children born in Ohio. This roughly consistent with the 1794 birthdate given for Samuel.
THEORY: William and Elizabeth are the parents of Robert. FLAW: William had a sister named Elizabeth.
Census page 1 and page 2.