I would suggest looking at the Olympus TG-2IHS or TG-830IHS. They are not out yet; however, they have the same sensor as their SLR cameras, which I know take amazing low light pictures.
I have had a chance to play with the TG-1, which does a great job, so I would think the newer models will do even better.
I already have the 830 on preorder (Both come out March 31st), as I like some of the features it has, such as being able to take pictures while taking video and such.
They are both designed for low light situations, one of it's many solutions is to quickly take multiple shots at different exposures and merge them together (I am not sure how well this will work on a dark ride, I suppose it depends on how quick it is).
They both have a shutter speeds of 1/2000 sec for the fastest time.
I currently have a Panasonic DMC-TS3 (which is f/3.3 to f/5.9), which does a good job with the dark rides. The 830IHS is f/2.9 to f/5.9 and the TG-2 is f/2.0 to f/4.9.
Here are some dark ride examples from the Panasonic Camera:
The three above are some of the very first pictures that I took with this camera, we went to
Disneyland to test it out and it turned out that it was a AP preview day for the Little Mermaid that day, which we were unaware of. Silly me, bringing a new camera that I know nothing about onto an attraction, which is a dark ride and is hard to take pictures of. But it worked and no, not every picture turns out, but enough do that I am good with it.
Here are a few more examples (NOTE: The Big Thunder ones are while on the ride and not during or just before the lifts):
Please note that all of these were taken without the flash. It also takes decent pictures with a flash.
Since the specs are not as good as the Olympus, I am looking forward to what the Olympus can do. I will try to report back here after I get it and play with it. Please note that the TG-2 is $379 and the 830IHS is $279.
As an added bonus, both cameras are waterproof, crushproof, drop proof and freezeproof. In other words, perfect for theme park travel.