How wide is the belt? A common solution in radio circles is to cut a length of O-ring material, place over the pulleys, hold the ends tight, and super-glue them. Sounds tacky, but I have O-ring belts that have held up for years.
Unless the belt is really wide and flat, the round stock works fine. Square stock is available, but it tends to climb out of the pulley more than round.
You want the length so that you have to stretch it a tiny bit to glue the ends. Buy enough stock for two or three tries, in case you don't get the tension right the first time.
An alternative would be to find a flat belt longer than needed, and trim & superglue at the right length.
Phil