Check with locums companies, many have openings for weekend night hospitalists that they, and the groups looking for help are more than happy to have resident cover for them,and have someone on sight during those times. Just need to have your permanent license which you can get after intern year, and completing step 3. Not to mention when you go to interview for a real job, they love that you've actually had real world experience, making your own decisions, not babysat or ruled over by like a peasant by some know it all attending.
moonlighting = money for you the resident, extra help and more time off for the group.
Personal experience: make about 120K my final year (45k through residency, and about 80K through moonlighting) and that's only 3-4 shifts/month.
Find somewhere that pays well enough to make it worth your while. They are everywhere, just have to start looking. No less than 85/hr to be onsite.