When as a result of a marriage, state employees are in violation of the prohibition established by § 8-31-103, such violation shall be resolved by means of such transfer within the governmental entity, transfer to another governmental entity, or resignation as may be necessary to remove such violation. The appointing authority of such governmental entity shall advise the employees of each of the alternatives available to remove such violation. Such employees shall be given the opportunity to select among such available alternatives. If such employees are unable to agree upon any such alternative within sixty (60) days, then the appointing authority shall take appropriate action to remove such violation.