Start a game, and at the character select screen, simultaneously press and hold L2, L1, R2, R1, and then enter any of the following cheats:

Alternate Bart - O, X, square, triangle
Alternate Frink - X, O, triangle, square
Alternate Homer - triangle, O, X, square
Alternate Krusty - O, triangle, square, X
Alternate Lisa - square, triangle, O, X
Alternate Marge - X, square, triangle, O
Alternate Nelson - triangle, square, X, O
Alternate Otto - square, X, O, triangle
Alternate Wiggum - triangle, O, square, X