I will ditto the suggestion of Recallers games, there's probably several in there that would be good inspiration.
With Payton one thing we worked on a lot as a puppy was a good release off a tug. Wild, furious tug games and a very strong out/drop command. IYC came into play because I would literally dangle the toy in front of him, put it on his head, et cetera and until I said "okay" he was not allowed to grab the toy again. This is fun for me because he is good at it - but you need to make sure students don't make it too hard/set their dogs up to fail, and either they or you as the instructor needs to be really good at identifying when it's gotten too hard and you need to lower criteria and make it easier so the dog can be successful before you pump up the intensity again.
I also agree about the two ball/two toys game. Very much about "the toy we are playing with is the one in my hand, so forget the other toys on the ground."
If you're looking at body awareness games I think a really good one would be teaching a 2o2o on a wobble disc, or maybe one of those new K9 Fit Bones, and then apply IYC with a toy (or food) here too. Slapping the ground with a toy, dragging the toy in front of them, dropping treats on the floor, and until the release is given the dog has to stay in 2o2o, then a riotous game upon release.
For a sports class I would also consider starting with obstacle discrimination. The Mary Ellen Barry foundations DVD actually talks about this in terms of tricks away from real agility obstacles. For her demonstration she has people shape their dogs to climb into a basket/box, and then go underneath a chair... then the discrimination comes into play when you cue the dog to do, say, the basket, even though the chair is right there. I think this is a really good idea and also like the idea of doing it without equipment. Not impulse control so much as stimulus control though I personally feel the two are related. In a class scenario I think we would start this the very first week to make sure they have time to shape the behaviors as homework, then come back the next week to address problems, third week to start the discrimination part.
I would also elevate this to using some of your body awareness tricks - either get on the wobble board or the balance disc depending on which I have cued. Then probably bring in a tunnel and ask for discrimination with/against the tunnel. At a foundations level I don't think I would even use a jump, but if you have a repeaters class or a second level, at that point I could bring out a jump.
Another idea would be teaching left and right spins and asking for these in succession, switching direction on command. You can also use this for wrapping a jump standard either to one direction or the other.
For me impulse control is an active activity, not a passive one, especially when talking about sports. I don't want my dog to think choosing impulse control is boring, I want them to think impulse control means the game is only going to get better as soon as they get released. OTOH I'm still struggling with a dog who doesn't really want to stop for contacts in agility... so take that for what it's worth.
I would also add that this sort of thing can be stressful for soft dogs. I showed a friend of mine the weave pole proofing I did with Payton (the toys and steak all over the ground) and she said "wow, that would be really stressful for mine, I think he might shut down if I asked him to try that." I told her understood that, and I had my limits on how far I was going to push Payton. I am not, for example, going to ask him to weave while waving steak in his face. That is a lot of pressure for what I personally feel is very little value to our training (I am never ever ever going to be at a show where he will need to weave while somebody throws steak in front of his face.) So just be aware of the dogs in your class and be careful about pushing dogs further than they are comfortable going. Some students may not recognize their dog shutting down and being overly stressed, so you have to be prepared to be an advocate for the dog and issue a break if you see the dog is getting "too much."