In order to get these cheats to work, go to the match-up screen (as the game is loading) and press SQUARE (first position), X (second position) and CIRCLE (third position) the required amount of times to unlock the corresponding cheat:

Log Bat: Square (0) - Triangle (0) - Circle (4) Up
Rubber Ball: Square (2) - Triangle (4) - Circle (2) Up
Extra Time: Square (1) - Triangle (2) - Circle (3) Up
No Fatigue: Square (3) - Triangle (4) - Circle (3) Up
Rocket Park Stadium: Square (3) - Triangle (2) - Circle (1) Up
Roman Coliseum Stadium: Square (3) - Triangle (3) - Circle (3) Up
16 Softball: Square (2) - Triangle (4) - Circle (2) Down
Unlimited Turbo: Square (4) - Triangle (4) - Circle (4) Down
Tournament Mode: Square (1) - Triangle (1) - Circle (1) Down
Mace Bat: Square (0) - Triangle (0) - Circle (4) Left
Maximum Speed: Square (0) - Triangle (0) - Circle (3) Left
Maximum Power: Square (0) - Triangle (3) - Circle (0) Left
Maximum Batting: Square (3) - Triangle (0) - Circle (0) Left
Small Heads: Square (2) - Triangle (0) - Circle (0) Left
Wiffle Bat: Square (0) - Triangle (0) - Circle (4) Right
Big Heads: Square (2) - Triangle (0) - Circle (0) Right
Pinto Team: Square (2) - Triangle (1) - Circle (0) Right
Eagle Team: Square (2) - Triangle (1) - Circle (2) Right
Lion Team: Square (2) - Triangle (2) - Circle (0) Right
Horse Team: Square (2) - Triangle (1) - Circle (1) Right
Todd McFarlane Team: Square (2) - Triangle (2) - Circle (2) Right
Terry Fitzgerald Team: Square (3) - Triangle (3) - Circle (3) Right