This probably won't help much, but the only MK restaurant I know for certain that has pizza is the Crystal Palace. In the kids section, for lunch & dinner, they usually have pizza, mac&cheese, etc. I would look on AllEarsNet's section that has all the WDW menus for your pizza info.
Oh, I just took my own advice & also wanted to know myself, so here's what could find out...
There don't seem to be any counter service places in MK that serves pizza.
Tony's serves some pizzas, but they might be too frou-frou for your picky eater.
If all else fails, you could always hop a monorail to one of the resort snack/counter service places - Capt. Cook's at the Poly serves pizza, so does Gasparilla Grill at the Grand Floridian.
If you're really stuck and pizza is one of the few things your picky eater can stand, maybe you could take some Lunchables "pizzas" with you? (but they do need to be kept cold).
Still take a look at those menus - maybe you can find some other in-park choices at MK.
Hope that helps,
agnes!