Every rollercoaster I've been on has a spot for putting down anything you're carrying. It's usually just a cubby, and on coasters with more than one train they're labeled by train so the ride attendant can at least stop people from taking stuff from the wrong train's cubbies. It's obviously not 100% secure, but I think it's rare for stuff to go missing from there, I've certainly never had anything stolen, nor have I heard any stories from friends of it happening.