Had this called to my attention. Seems there are two statutes that might apply when a seat on the council becomes vacant. This one says, if you scroll down to section e, that the mayor appoints a replacement to the council, which the remaining council members vote to confirm or not within 60 days. If the mayor's appointment is not confirmed, the mayor selected and forwards a second one, which the council must confirm or reject within 30 days. If this one is not confirmed, the mayor then appoints one of the two to serve until the council confirms a candidate or the position is filled by election.
However, this statute says, in section g, that the council shall appoint a replacement member, with no mention of the mayor making the appointment. I imaging the council will be seeking the counsel of lawyers before making any decisions regarding how to proceed. Isn't politics fun?