If your children have foul-smelling sweat before the onset of puberty, chances are they are trying to detox something they are reacting to, and I would seek out an allergist or homeopathic dr. to get to the root of the issues instead of "masking it" with scented deodorant.
Having said that, I try to limit chemicals that my kids are exposed to, and body products are no exception. There are several safe "Crystal" and herbal deodorants on the market, or simple recipes to make your own at home (coconut oil and baking soda, for example.) If you have problems finding these, go by a health-food store, as they usually stock them as well.