I don't have a child with Downs either but I do have an aunt with Downs and my best friend's sister has Downs. I think that a reward system might work just as it might work with any child but I think it would have to be some kind of immediate reward otherwise I think they would probably forget about it. Like someone said about a chart with stickers and then a big reward at the end, that might not work because I don't know if a child with Down's would remember something like that and they might not be motivated enough by it. I think if you used a reward system that they got some kind of reward everytime they used the potty then it might create a form of habbit knowing they wanted that specific thing and knowing that if they used the potty that's the only way they would get it might help. Good luck with it!