If both players want to use the same character in the two player mode, use this code. At the title screen, press down, down, up, up, right, left, right, left, L, R on player 1's controller. If entered correctly the background should change color from black to blue. Now, when you enter the character select screen, both players will be able to choose the same character.
To prevent confusion, each character has a second costume colour so you can easily tell who is playing as who.