There are many types of drivers, and Chuck is right, you will want to make sure they are the same, or that you find a solution that deals with whatever each one is together. You might be able to follow the traces on the PCB and find out, or do some testing to find out.
Usually one side or the other will be switched, and you don't know if that switch is a push/pull type of switch that can source or sink current, or whether it is a switch that allows current or disallows current.
Controller 1 anode (usually red)
Controller 1 cathode (usually black)
Controller 2 anode (usually red)
Controller 2 cathode (usually black)
I would begin by trying to see if the cathode of both of the above are directly grounded. Maybe follow the PCB. Measure ohms between it and a ground plane and if they are direct connected, you should be able to use the Schottky diodes on the anode sides. Connect only one cathode side (both are ground).
You could do the same thing with the positive rail. If both the anodes are connected to the 5V rail directly, just connect one of them to the anode side of the LED. Then use the Schottky diodes on the cathode sides to only allow power to go one way.
If it is something different post back!