Maybe you could try a star chart during the week and if she gets XX stars for the things she's supposed to do, good behavior, she could stay up 1/2 hour on saturday night and do something special like popcorn and a video or read her favorite book etc.

BUT, there'd have to be a rule, that at 9:00 if you have a fit, you don't get to stay up the next Saturday.

She's 7, she should be able to grasp that idea.