A lot of people who have problems with parallel bar dips find they can do them on wide-set rings or Blast Straps without pain.
However, prepare to be humbled the first time you try them because it's a whole different ballgame than regular dips. When I first tried them I could do regular dips with four plates for reps so I'd figured it'd be a breeze. Wrong. I made a complete fool of myself and couldn't even do one rep. After about an hour of practice I could knock out a whooping 3 reps while shaking so badly it probably looked like I was being electrocuted. And that's with no extra weight.
Swallow your pride and stick with it because after a few times of getting acclimated to the rings, it gets much easier and your performance will shoot right back up.
Start with the rings set just outside shoulder-width so your triceps can press against them for support. As you improve, try moving them wider to increase the difficulty and chest stimulation.
To keep constant tension on the chest, stop an inch or two short of locking your arms out at the top. This may seem like it's cheating, but with rings set wide it actually makes it quite a bit harder.