Quite frankly, your best bet is to consult a physical therapist so as to avoid injury. Outside of that, one physical therapy site recommends the following:

1. Avoid overstretching
2. Avoid positions or activities involving extreme ranges of motion in the hips
3. Strengthen muscles surrounding the hips, pelvis, spine, and knees (best to be advised by a physical therapist. Pilates exercises may also be a good option.)
4. Consider pool exercises/swimming and/or biking as a low-impact means for strengthening your joints within a normal range of motion.

Quite frankly, your best bet is to consult a physical therapist so as to avoid injury. Outside of that, one physical therapy site recommends the following:

1. Avoid overstretching
2. Avoid positions or activities involving extreme ranges of motion in the hips
3. Strengthen muscles surrounding the hips, pelvis, spine, and knees (best to be advised by a physical therapist. Pilates exercises may also be a good option.)
4. Consider pool exercises/swimming and/or biking as a low-impact means for strengthening your joints within a normal range of motion.

On a side note, I had a roommate who suffered from overly lax ligaments (possibly as a consequence of Marfan Syndrome) and he got a lot of enjoyment out of volleyball and frisbee, although he gets most of his exercise by working on his farm. He enjoyed the double-jointed parlor tricks, but mentioned that he gets joint pain really easily, which is why he never did any sort of running.