R.H.
If you know that his asthma is induced only by exercise, and if it is predictable and mild, then perhaps you could take him off of the Flovent completely and just treat him "as needed" with albuterol just prior to, and possibly during, athletic activity. It will depend on how bad his asthma is. Asthma does evolve over time, sometimes getting worse other times getting better and even resolving completely. Perhaps you could ask the Dr. about using this time to see how he does without the Flovent. Obviously you know your son better than I do (or the doc for that matter) so if you think it would be too risky then don't do it, and definitely don't do it without discussing it with the doctor first.
THere are other asthma inhalers, but the other corticosteroid inhalers (like Flovent) might have the same side effects because they're in the same class. Any other type (like Advair) would be for more severe asthma. I think you'll probably either have to stick with the Flovent or try just using a "rescue" inhaler for those predictable times when symptoms are likely to occur.