I am no expert on Michigan politics, but I’m sure I read somewhere where Michigan Gov. Rick Snyder has some say as to filling the vacancy with a special election, or does Conyers get to pick his successor....Pretty sure the Gov has some say....
The US Constitution prescribes that the state governor call a special election to fill a vacant House seat. In practice, if the vacancy occurs in the second session of a Congress, the seat is usually left vacant until the next general election.
It would seem to depend on the exact timing of Conyers’ official resignation. We’re close to the end of this Congress’ first session.