Only problem is the best GOP candidate for the seat IS the Governor.
If such a situation happened in West Virginia I know that that govenor would appoint himself in a heartbeat.
Were Gov. Rounds to ask me for my advice, I would recommend Bruce Whalen, a Republican Oglala Sioux who ran against Stephanie Herseth (D) for SD House in the last election. He lost the election, but is a good guy. Solid Native American conservative...........but Stephanie is much prettier.
He's probably not precluded from appointing himself, assuming he wanted the job. Then they'd probably have to have a special election to replace him as governor.
--Only problem is the best GOP candidate for the seat IS the Governor.--
Is there anything in the State Constitution preventing him from appointing HIMSELF?