It has been rumored there is a way to fix the Tiny Bronco on the third disk. Win the Super Sweeper from the Golden Saucer, go to Junon and talk to everybody. Cid will then realise he can use the Super Sweeper to fix the Tiny Bronco. Go back to Cid's hometown (Rocket Town) and he'll fix the Tiny Bronco, which you can use now.

NOT CONFIRMED