On Friday, Hinckley developer David Terry pleaded guilty to paying Coyne $20,000 in bribes.
Coyne has not been charged with a crime.
Coroner's spokesman Powell Caesar said the action was taken to preserve the office's integrity and reputation.
Coyne has never been named in legal paperwork. But others have acknowledged he is Public Official 17.
Terry admitted paying Coyne "to influence and reward" him for various matters in 2007.
Coyne formerly worked for Cuyahoga County Prosecutor Bill Mason as budget director.
Caesar said reorganization plans call for Coyne's position to be abolished, with duties being reassigned.
Coyne is an at-large member of Strongsville council.