What kind of doctors specialize in children with rare diseases?

It Depends: It really depends on what kind of rare diseases they have. Pediatric oncologists deal with rare cancers, nephrologists deal with rare kidney diseases, cardiologists deal with rare heart diseases. Geneticists probably see the most patients with rare diseases, but i'm not sure that's what you mean by "deal with".

Not rare disease MD: It's the rare disease in whatever area the disease exists in--the rare heart disorder, the rare cancer, the rare skin disease, etc. Fully-trained and board-certified peds cardiologists, oncologists, dermatologists, would be able to treat not only the routine and everyday cardiac, cancer or skin problems and diseases, but also the rare or unusual ones. Some will be better and smarter than others!