Offer $1 billion to orbit an unmanned (man rated) capsule around the Moon. Then another billion to land same capsule. $5 billion to land a crew of two, and return them to Earth. Since each is incremental, the risk for the companies trying to compete will be lower.
EDIT: Yes I know the costs are far higher than the prizes I'm mentioning. It's the general concept I'm aiming at.
There is also a controversial "Apollo Heritage Bonus Prize" of $1M if a team's robot visits one of the Apollo landing sites.