There's nothing for really picky eaters. They don't offer a "kids table". The only kid friendly options are mac & cheese and authenic german frankfutters. Some say kids will eat the roasted chicken, but unless it's breaded, my son wouldn't touch it.
Due to the lack of kids food, we haven't been there with our children. My DS2 would eat anything, but DS5 is a fan of the typical WDW Kids meals of pizza, nuggets, burgers and fries.