Is there such a thing as an automatic variable resistor
Measure both coil resistances. And the joystick voltage. With that known it may be possible to work out how to trim out the error.
Based on your current question it sounds like a 50mA constant current sink could be a quick and dirty solution. However i am left suspecting its a voltage driven joystick. And the resistance is lower on 1 coil
Having measured both coils if you find there is a difference. Then adding series resistance to match it back up may resolve your issue. Otherwise with that information it may be possible to design a solution.