I've read vitamins A and C are needed by the immune system to function well. For vitamin C, the dosing instructions I got (and use) are 50mg/kg body weight per day when healthy and 250mg/kg body weight per day when sick/getting sick. That last translates to 1.1g per day per 10 pounds of body weight, which seems like a huge amount, but I've seen it be well-tolerated both in myself and my daughter (a bit under 40 lbs, I think). It needs to be spread out as much as possible throughout the day, like take some every hour or two. The sodium ascorbate version of vitamin C is easy on the body and very mixable in plain water or other drinks--it just tastes salty.
Although I aspire to a healthy lifestyle that doesn't depend so much on supplements, for now we take the vit C "maintenance dose" every day, 2x/day for my daughter and split into 3 or 4 doses for my husband and me. I think that has helped, but that's harder to say.
Since I started using the vitamin C for us regularly, our colds (my kids, almost 3yo and 7mo, are in daycare in the morning) have gotten dramatically shorter and milder. It seems easier to get enough into the baby since he's nursing (I just take tons and give him a little directly a couple times a day) so when he gets a cold, I wipe his nose about twice a day, and other than that, you couldn't tell he's sick. None of that poor sleep and trouble nursing due to congestion--I've been so grateful (and wished I knew about it when my daughter was a baby). It's been a bit harder to get that high a level into my daughter, but I still notice a real difference in her colds.
I don't know much about vitamin A but if I was having lots of sickness, I'd start at the NIH site below and consider supplementing at the tolerable upper intake level for a while with cod liver oil.http://www.ods.od.nih.gov/factsheets/vitamina.asp
I've taken my kids to a doc who is a chiropractor and does applied kinesiology (I don't know how to separate what he does into the two buckets). Honestly, it's really, really weird, but based on results I've seen, I've converted from interested skeptic to totally fascinated in what he does and how it works (I don't get it yet). One who's used to working with kids will be able to deal with them just fine I'd think--mine didn't make my daughter lie down at all, I don't think, and he was quick (and entertaining).