Keene, OhioKeene is an unincorporated community in central Keene [Township, Coshocton County, Ohio|Keene Township], Coshocton [County, Ohio|Coshocton County], Ohio, United States. It has a post office with the ZIP code 43828.HistoryKeene was laid out in 1820. A large share of the early settlers being natives of Keene, New Hampshire, caused the name to be selected. A post office called Keene has been in operation since 1825.