For Steel coasters you can do some handy work and get a really good tight grip clamp. If you can get one that applies a GOOD amount of force, you can possibly get permission from parks that otherwise wouldnt let you. (like Paramount or Cedar Fair)
Otherwise, you do just need to hold on. I prefer to hold it against my chest firmly, but not too firmly. Let the forces move the camera around a little bit to dampen the blows, but not too much.
As for wooden coasters, 3 words. Wide Angle Lens. The wider you get, the more stable your shot will be. Why? Because your FOV is wider and not so narrow. Thus, when the camera shakes its filtered out through the wide angle of the lens.
You can apply this theory easily. Take your camera, zoom as far in as you can go and shake it. Then zoom back out and shake it the exact same amount. Because you are zoomed it every movement is magnified. So, a wide angle lens will increase your FOV and give a much more stable shot.
Thats how Robb Alvey's wood coaster POV's come out so great. ACN uses a mount for steel coasters but his wooden ones arent too good because his lens isnt wide enough.