I've wondered if it's worse as adults partly because we have such resistance to changing our daily routine, slowing down, and taking care of ourselves as adults. And we're responsible for making our own food and taking care of the basics as adults--kids are taken care of (as they should be, of course).
Vitamin C has helped with almost all of my kids' illnesses (not sure if ever helped with diarrheal illnesses), and I think A helps with rash illnesses in general, though I agree it's more with measles.
I'd think general stuff too--vitamin D status (overall immune function), a diet that's meeting their needs, low stress in general.
We haven't had CP yet, I sorta hope we can wait a couple years, I'm working on health stuff for my kids (and myself) and I don't feel ready yet. But those are part of what I'm envisioning.