I suspect that your main problem *may* be that you are chasing the aeroplane.
Slow your pedal inputs down, use small slow corrections, and ease - not force, the aeroplane to the centreline.
Actually, this is the best way to get an aeroplane to any condition you want - taxiway centreline, heading, height, etc. etc....
If you wish, I can explain the theory behind this, but try it first and see if it helps.
G