RONR 11th edition has a new section in the chapter of “Discipline.” It is called “Removal of Presiding officer from Chair for all or part of a session.” It gives a way to temporarily replace the chair when he is not fulfilling his role when conducting a meeting. If the person presiding is a chairman pro tem, he can be removed by a motion to “declare the chair vacant and proceed to elect a new chairman.” RONR states that this is a “question of privilege affecting the assembly and is an incidental main motion requiring a majority vote for adoption.” The procedure is in the first footnote at the bottom of page 652.
If the presiding officer is the official officer, then the procedure is different. A member must make the motion to Suspend the Rules to take away his authority to preside during part or all of the meeting. A motion to suspend the rules can’t be made for future meetings at the present meeting. It would have to be made at each meeting the assembly wanted someone else to preside.