Invite people to sit inside their stores with discounts and offers. That way they can just use their mugs and wash them and reuse them again and again.
offer an incentive for people to use reusable cups. i'm pretty sure that they sell reusable cups in their standard sizes, so maybe offer a free drink with the purchase of a reusable cup (they'd have to wash the cup first though) and/or 10% off drinks if using a reusable cup. people use paper cups because they are convenient, so there needs to be something that is better than being convenient to get more people to stop using paper cups since the vast majority of people won't care otherwise
Close the store
Use recyclable plastic cups. "Serve" the coffee like a water fountain set-up ... with different fountains for various options.
Switch to plastic cups.
Offer ceramic cups for in-store consumption.
Give a small discount or a point toward a reward, or something of that nature for people who bring in a store-purchased travel mug.
Update --> That is to say, a reusable mug or thermos.