On the Player Select screen, highlight your driver and simultaneously press Y and A.
The only way to change back during a race is to hit a mushroom dropped by the Princess.
Note: this will not work in Time Trials or Battle Mode.
On Controller 1, begin a one-player Time Trial.
When you come to the driver select screen, press Start on Controller 2.
Select a driver with Controller 2, and then select a driver with Controller 1.
Begin the race by pressing Start on Controller 1, and you will be racing against a CPU player.
Enter the Time Trials and select your racer.
Then push Left on your controller to move the cursor beside "Mushroom Cup."
Then press L, R, L, R, L, L, R, R and A.
You should see "Special Cup" appear below "Star Cup."