Unfortunately it's a hard problem with no easy, performant solutions.
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So the two players screens both show up, but you can't control player 2 with a controller? 2/3/4 players requires a plugged in controller and it's recommended that you use an xbox 360/one controller.
Does the controller work in other games, because if not you need to install a driver: http://www.cultofmac.com/198535/use-your-xbox-360-...
If the controller does work with other games can you try unplugging it, restarting your Mac, starting Planet Deathmatch, and then plugging it back in.
It's untested but if it's a dualshock 3 then it should work with BetterDS3: http://betterds3.ciebiera.net/ as it can bind it to virtually any input device including Xinput and mouse/keyboard. If it's a dualshock 4 then it should work with DS4Windows: http://ds4windows.com/ as it emulates an xbox360 controller.
If you have tried it, I would love to know how well it works as I don't have either controller available to test it on. However, assuming it works, any controller button prompts may be incorrect.