“Save Tree” Campaign
You have to give a reason for people to reuse their cups. Carbon Fiber cups are capable of not only hot drinks but also cold. Therefore, the cups should be reusable for about a week.
In addition, the bottom of the coffee cup can be foldable so it can be recycled easier, takes up less space and a bit more "attractive" so people may be more likely to reuse it.
Starbucks rolled out their EarthSleeve in 2012 which helped saved 100K trees per year. The problem with EarthSleeve is that is goes in the garbage along with the cups.
There could somehow be a stamp-reward system in which people KEEP the EarthSleeve along with the cup they originally had and for every 10th drink, they get the next one for free.
Nowadays, people enjoy being a part of something larger to make an impact in the world. If you somehow made it fun for people to reuse cups, but also show them that they would be helping the environment as well in a visual manner, they would be less likely to throw away the cups.
An idea would be the “Save a Tree” model in which the cups have a name of a tree that it was created from. That way, people would somewhat have a connection with that cup. Just like how Coca-Cola have names on their bottles, a similar concept would also be approached. Not only would it be socially popular (things tend to spread like wildfire when it’s unique and weird) but it would also bring awareness to people.