I have a plastic covered chart that I bought at Powell's books, listing all the vits, minerals and how they help the body.
Zinc is in cooked oysters, beef, lamb, eggs, whole grains, nuts, yogurt, fish, legumes, lima beans, mushrooms, pecans, pumpkin and sunflower seeds, sardines, soybeans, and poultry.
You could also add a zinc supplement to his/her juice.
Some surprising foods have Vit C. Broccoli, cantaloupe, kiwi fruit, pineapple, peppers, strawberries, asparagus, avocados, collards, dandelion greens (young ones are delicious)kale, mangos, onions radishes, watercress and of course the citrus fruits.
My daughter's sister also uses herbs to keep her kids immune system healthy. I have a chart entitled Herbal Therapy made by the same company that made the one on vits and mins.
Echinacea, golden seal, and garlic are good to prevent and also to treat colds. She also uses bilberry syrup tho it's no listed on this chart.