It's kind of... annoying, you could say. First, make sure the stick is properly calibrated in Windows (if you have a utility called DX Tweak (it should be on your Wingman software CD), you can compare the calibration-values to what you really get). Then, open dark.cfg and check the calibration-values there. Adjust where necessary. If that still doesn't work (DO NOT RECALIBRATE IN P2! That'll negate your efforts with dark.cfg), just increase the values in dark.cfg by maybe 2 or 3. That should improve things. Otherwise, using the mouse is a viable option.
[Edit] Uh, assuming you're playing P2 Win95-edition, that is. If you're playing the DOS-version, I suppose you'll just have to assault dark.cfg right away.