The 1880 Ohio Census lists Davis Randolph and his wife Caroline living in Beaver Twp., Mahoning Co., Ohio on page 25B. (National Archives Film T9-1045). (Beaver Twp. is on the southern border of Mahoning Co., adjacent to Columbiana Co.)
Davis is listed as Justice of the Peace, age 69, born in Pennsylvania, father born in New Jersey, mother born in Delaware. Caroline is keeping house, age 60, born in Ohio, father born in PA, mother born in Virginia.
John and Mary Jane would almost certainly be dead by this time, and neither is listed in the 1880 Census Index. It would seem likely that they would be buried in Beaver Twp., especially if they were living there in the 1850 Census.
Since Davis was a JP, there may be records mentioning him in the Mahoning County Courthouse, 120 Market Street, Youngstown, OH 44503, Phone 330 740 2130 or 330 740 2314. At least it may be worth a call to see where records from that era are stored.
There MAY be Cemetery records from Beaver Twp. at the Public Library of Youngstown and Mahoning Co., 305 Wick Ave., Youngstown, OH 44505-1003, Phone 330 744 8636, email firstname.lastname@example.org.
I hope that at least some of this is helpful to you.