Depending on the orientation of a nulling coil I need an adjustable voltage supply from ~+5V to -5V upto ~200mA. I've tried a few circuits similar to Class AB amplifiers such as the one shown below, but these normally expect an AC coupled input. Has anybody got any other suggestions?
You may want to consider a unipolar to bipolar level shifting circuit that is based on a power op amp. An example schematic is shown below. Instead of the DAC, you could simply use a potentiometer.
Regarding calculations, there is a good application note here, which should help you hit the ground running.
Keep in mind that you will need to ensure that the op amp can source/sink the necessary load current.