A friend with 7 slipped discs joined us last year and this is what we described to her so she could pick. This is in no way a full list, we didn't ride everything else and you should find out more before you jump on anything else. We didn't even go into animal kingdom so take others advice on what may or may not work for you. I do remember a lot of bumps on some of the see the animal rides, but I also remember a few that were on a track and those should be ok.
- Space Mountain - boardwalk like little coaster with a lot of fast jerks and in the dark so you can't be prepared before they happen. This ride actually cracks my back for me most times and usually my favorite first as it's cheaper than the spa

- Big Thunder Railroad - a lot of bouncing and uses a bar across 2 people to hold you in. There is a couple quick changes that will stretch or compress your back not to mention the side to side motion since you can slide with the bar style "safety belt"
- Tower of Terror - free fall elevator ride, you will float and compress really hard
- Rock n roller coaster - disneys first coaster with upside down loops, it will push your shoulders and full body weight into the harness when upside down or the really steep turns it makes.
- dinosaur - you get tossed all over the place simulating off road conditions. don't even consider this one.
- the smaller carnival like rides next to dinosaur - small track, you can see them to decide for yourself but a combo of small coaster and tilt a whirls.
- test track - there is a couple spots with hard breaking and fast swerves to avoid things. I would question if this would be ok.
- mission to mars - G force simulator turned into a ride. It's going to push you back into your seat for almost the entire ride.
- Everest - not sure about this one, backwards roller coaster for most of it. I do remember some bumps but not sure if it would be a problem. think twice about this one.
What we didn't skip that you may not realize might be ok:
- 7 Dwarves mine train - I only recommend this if you wait to be in the front of the coaster (tell the CM who is telling you where to sit). At the top of every climb up is a small up and down track movement. If your in the front, the back still climbing has you gently go over that bump and really takes away from the ride but as someone with a back concern, that's the only spot I would worry. The cars freely rock side to side and really makes it gentle vs other coasters.
- Splash Mountain - This was our friends favorite. I never really thought of it but it's a smooth transition to the water drop and the water offers some padding to gently slow the ride at the bottom. She had no issues and road this as much as they would let her and has become here try to stop me from going again ride.
- Kali River Rapids - *** This may not be ok *** - It's a really gentle river ride but it's a free roaming group raft and can push into the sides with some force and jerky motion. This type of injury I would think twice before getting on.