The original belt should last quite a while if it is adjusted properly and you are not overloading the tumbler. In a pinch "standard" size 1/4" wide rubber bands work as belts too, but long term use of them can damage the plastic pulleys.
Make sure you adjust the spacing of the two pulleys (yes, this is adjustable) to be just enough that the belt is not too loose (i.e. it just catches). This keeps the belt at the right tension and not too tight. If it is too tight it will work, but it will stress the belt.
Don't overload the tumbler. It is rated for 3#. If you are filling it to the brim with coins, rocks and water it is too full and too heavy. This stresses the motor and the belt. Ideally the tumbler should be no more than 1/2 full of rocks and coins and no more than 3/4 full when you add water. Besides saving the motor and the belt life, a properly loaded (not overloaded) tumbler works better and faster at cleaning your coins as the material has room to move around in the drum.
Replacement belts can be located cheaply on eBay and are typically as good or better than the original belt. Many rock shops and lapidary stores sell them in retail stores and online too.