Diet is always a good place to start, as with children some of these changes may be difficult for them. Limit sugars, soda, choc., pizza, anything with red sauce, fast food. Avoid "box" food and opt for fresh food instead. Avoid red meat, spicy, deep fried or greasey foods. Introduce lean meats chicken, turkey, fish, green veggies, sprouts, some ppl can eat eggs. Melons are great as well (watermelon etc...).
Supplements.....hmm, I'm always careful when it comes to children. Papaya (is like a natural tums) will settle a upset tummy and is safe. Manuka honey (with warm water as a tea) soothes throat and tummy. Childrens multi-vit can't hurt either. Digesitve enyzmes and probiotics are an option, however check with your childrens dr to make sure it's ok to give (children are differnet than adults).
This should get you started in the right direction, as you don't want to introduce too much at once.