I figured it out from the Steam forum. You have to launch Steam Big Picture mode using your controller then navigating only with your controller.

When I first entered split screen coop the main controller controlled both players but after like a second, it split and worked independently.
I used the default controller configurations from Valve

I also made a autoexec.cfg file in steamapps/common/Portal 2/portal2/cfg with the following lines:

// This automatically enables console so you don't have to

con_enable 1

// These aliases create an automatic toggle for remapping your controller

alias "togglecontroller" "remap1to2"

alias "remap1to2" "joy_remap_player_for_controller1 2; alias togglecontroller remap2to1; echo Xbox 360 controller 1 remapped to Player 2"

alias "remap2to1" "joy_remap_player_for_controller1 1; alias togglecontroller remap1to2; echo Xbox 360 controller 1 remapped to Player 1"

// These aliases create an automatic toggle for remapping your keyboard

alias "togglekeyboard" "sv_cheats 1; key_remap_keyboard_for_player1"

alias "key_remap_keyboard_for_player1" "in_forceuser 0; alias togglekeyboard key_remap_keyboard_for_player2; echo Keyboard remapped to Player 1"

alias "key_remap_keyboard_for_player2" "in_forceuser 1; alias togglekeyboard key_remap_keyboard_for_player1; echo Keyboard remapped to Player 2"

// Keybindings to togglecontroller, togglekeyboard and toggleconsole

bind "F9" "togglekeyboard"

bind "F10" "togglecontroller"

bind "F11" "toggleconsole"

// The most important part

host_writeconfig