Bucks for Stars
Basic idea: Encourage reuse. Every papercup gets a star-shaped stamp. If you bring it in to refill, you get another stamp on it. Every star gives you a refund on your coffee. Once you have 5 stars, you get a fresh papercup with your next coffee.
Why 5: because lots of people drink coffee on a daily basis, like every morning on every workday. That makes 5 papercups a week - and you start off every week with a fresh cup (something to look forward to in a monday).
Result: only 1/5 of the papercups used today would be needed. We can cut down from 58 billion to ~12 billion.