Other State Solutions for Vacancies
Arkansas -- Calls for the governor to appoint a new U.S. senator " until the people fill the vacancy by election at the next-ensuing general election," but if such an election is more than a year off, as it is now in Illinois, "the Governor shall call a special election to be held "no more than 120 days after the vacancy occurs."
Louisiana -- If the United States Senate is in session when the vacancy occurs, the governor shall appoint a senator to fill the vacancy within 10 days after receiving official notice of the vacancy....(If) the unexpired term is more than one year, an appointment to fill the vacancy shall be temporary. Any senator so appointed shall serve until his successor is elected at a special election and takes office. Within 10 days after receiving official notice of the vacancy, the governor shall issue his proclamation for special election to fill the vacancy for the unexpired term... If a vacancy occurs in the office of United States senator and the unexpired term is one year or less, no special election shall be called by the governor and, if a senator is appointed to fill the vacancy, he shall serve for the remainder of the unexpired term, and his successor shall be elected at the next regular election for United States senator.
Mississippi -- "The Governor shall, within 10 days after receiving official notice of such vacancy, issue his proclamation for an election to be held in the state to elect a Senator to fill such unexpired term as may remain, provided the unexpired term is more than 12 months... the election shall be held within 90 days from the time the proclamation is issued.... (If the vacancy occurs in) a year that there shall be held a general state or congressional election... the Governor's proclamation shall designate the general election day as the time for electing a Senator. ... The Governor may appoint a Senator to fill such vacancy temporarily, and if the United States Senate be in session at the time the vacancy occurs the Governor shall appoint a Senator within ten 10 days after receiving official notice thereof...(If the remaining time is less than a year, the appointee) shall serve for the full time of the unexpired term and no special election shall be called by the Governor but his successor shall be elected at the regular election."