My proposal has three elements.
1: Incentivise re-use.
Let us suppose that a cup of coffee costs $5. I propose increasing the cost where a disposable cup is used (say, to $6), and decreasing the cost where a re-usable cup is used (to$4). Some cafes in my area already do this.
The regular customer makes a saving by making the envirnmentally responsible choice, and the retailer benefits from their repeat business. Note that this proposal both rewards the behaviour we want, and penalises the behaviour we don’t.
When the re-usable cup is damaged, the customer may bring it back to the retailer and exchange it for a new one at no charge.
This keeps the system going, e.g., the customer continues to enjoy discounted coffee, and the retailer continues to receive their custom. More importantly, it ensures that the damaged cup does not go to the landfill – the retailer can ensure that it is properly recycled.
3: Cup Design
I propose that the cup have a stainless steel inner (for hygeine) and a cork outer layer. Cork is waterproof, an excellent insulator, is pleasant to the touch, and is of course a natural material. Why not cork only? Simply because it might be difficult to wash and might harbour bacteria over time.
A steel-and-cork sipping lid would fit snugly over the cup. Because the sleeve is slightly shorter than the steel cup, a sufficiently airtight seal may be achieved.
The main reason I propose this design though is that it is easy to separate out the technical and biological elements for recycling (the steel), and either recycling or composting (the cork).
My prototype uses corkoleum, a cork-and-rubber flooring material. This is probably too expensive for mass-production though.