Well, I've managed to get around the problem of getting my camera past the ride ops. I always ask for permission (or take advantage of known policy) before shooting on board a coaster. By not sneaking around, I can take suitable precautions with the camera before the ride starts.
I gave up on on-ride stills a long time ago because I was never really happy with them. But I have shot lots of on-ride video, most recently of The Legend at Holiday World on Friday evening. I use a small camcorder, small enough that I can hold it in one hand, and I keep the hand strap tight enough that even if I open my hand the strap can't slip over my knuckles. The camera is small enough that my hand wraps around both the top and the bottom of the camera, so it's literally going nowhere. I have a wrist strap I constructed specifically for on-ride shooting, which cinches around my wrist and attaches to the tripod socket on the bottom of the camera, but I keep forgetting to take it with me into the park.
When possible I prefer to hold on to the camera with both hands in order to get a more stable shot. Rather than bracing the camera against my body, I prefer to take advantage of the fact that my arm really is a sophisticated shock-absorbing, balancing system. Image stabilization on the camera seems to help a little, but good hand-holding is the real key. When shooting video you might want to pull the lap bar down an extra notch or cinch the seat belt up a little so that you don't have to concern yourself so much with stabilizing your body, and you can work with the camera instead. You'll find that hand-held video is usually more satisfying than the tied-down stuff they use on the TV shows because with the hand-held camera you can anticipate the ride elements visually. You can look down that hill when it comes, you can see the spiral drop coming, stuff like that.
--Dave Althoff, Jr.