Back in my high school fitness gym class, on days where I couldn't do the cardio things because it was a bad asthma day, I'd do weightlifting. Even a couple of cheap dumbbells could help, maybe? I'm afraid I don't know of anything else, though.
Piggybacking on this thread because I also have asthma and I have a hard time exercising. I also have mild asthma so what I do might not be useful to you nwn; I've found that moderately paced walks around my neighbourhood are good, but I can't do them in winter because the cold air is horrible for my lungs. I think starting off anything like say using a treadmill by going at a moderately fast but steady pace is better than trying to run on it.
