[Configuring Two XBox360 Controllers for two player alternating games]

Is it possible to use separate XBox360 controllers when playing two player alternating games like Pac-Man or Galaga? The way I've got them configured now, they work fine for multi-player games. Hoping to not have to keep passing the controller back and forth when switching players.

[XBOX360 Controllers - Second Controller]

First XBOX360 Controller works fine and I even have Player 2 start button working on the second controller. I've configured the second controller inside one of my MAME games, but when I go to play two players, player 2 controller doesn't work. Both players have to use player one controller. What am I missing??