Knee instability is usually as a result of one of two things - You either have a pre-existing injury that is contributing to the instability, or you have muscle weakness that is contributing. (This is assuming no congenital defects).
For the first, you may have to supplement with braces and/or corrective surgery. While you can protect the area with proper form, even a correct stance may make a pre-existing condition worse.
For the second (And to some extent the first), the stronger you can make the muscles/tendons that pass through/around the knee, the more external stabilization you will have. This may require supplemental weight training, which I suggest you do under the guidance of a certified (NSCA, CSCS, etc) trainer.
As far as the training, you can do pretty much any of the various agility drills with ladders, cones, etc. with the caveat that they will increase the chance of injury. Proceed slowly with great emphasis on correct form, so that as you eventually get faster your form stays correct. The pivot drills will be the most risky, as you are rotating around a fixed point, lateral movements would be the next step down on the risk factor scale, while forward/back linear movements are likely to be the least threatening to stability.
However, ANY training that is done at high or competition speeds carries its own risks, as even a slight misstep may cause a pre-existing condition to flare up or get worse. In the end, you need to really be aware of your own body and judge what might or might not help/hinder your progress.