I figured that since revolts exist, I'm surprised something like this doesn't exist. Essentially, a Coup d'etat for the Police would be initiated by a senior ranking Police (Ie: PD Commander, S.W.A.T Chief, Potentially Judge Gabe)
When a senior ranking police initiates a vote, other senior ranking officials are given the option to participate, each person adds a 20% change that the Mayor is overthrown, If the mayor is overthrown, the initiator immediately takes his job, If he fails, the Initiator and any participating officials are immediately demoted as if they were fired from the mayor.
Revolts/Unfun are done from the civilians for mayors that are too cop heavy, but a Coup d'etat would be a nice change of pace for mayors too criminally heavy. Hopefully this will encourage more mayors to be neutral and actually take all sides seriously.