Unfortunately, Carrera does a terrible job of stocking replacement parts including tires. Paul Gage makes some great replacement tires in urethane but they have to be glued to the wheels as they are not a very tight fit. Once glued, you can true them up and they are better than the stock tires. Slot Car Corner has a great Paul Gage tire selector where you can enter the car make and model and it will bring up your choices.
The Houston club runs stock Carrera cars and makes the Paul Gage tires one of the only things you are required to change.