What I would do is.. I'd make a schedule. People would choose time chunks that they enjoy streaming during. I would even try to always have a person "on call" if the first person couldn't make it.
So for example, say:
Lith can stream 8pm-10pm central MWF, I'd put him down.
DCook can stream M-F 8-10, she'd be A Streamer on T and Th, and B streamer MWF
People can change their stream times, but they'd just have to let me know in advance.
It would be like me making a work schedule pretty much for part timers.. I'd come out with the new schedule on Sunday, and people would have to let me know by Saturday night if they need off. If you don't let me know, you'd be responsible for getting someone to replace you.