Code: L1 or R1
After finishing the game on Golden Days, save after the credits. When you return to the main menu, go to Arcade Kings and the "Unlimited" option will be available. You can compete against the CPU or a second player using the cars that the CPU used against you (for example, Chill N62, and the car with horns).
After finishing the game on Golden Days and after the credits and video, save the game. Then, start a new game on Golden Days. You will have the '59 Impala along with the '61, '63, and '64.