This has more to do with where you work once an attending surgeon than the general field--assuming that you choose a surgical field that at least has a significant amount of pediatric disease and surgical treatments. With some exceptions, if you want to be a surgeon who operates 100% exclusively on children (< 18 years of age), you need to work at a bona fide pediatric hospital (usually something with "Children's" in the name). In most cases, these hospitals are wholly separate from their adult-oriented brethren and don't even admit patients who are 18 or older. There are very few community hospitals out there with enough pediatric business to keep a surgeon 100% occupied, even in kid-heavy fields like ENT. More commonly, pediatric surgeons will rotate through several community hospitals or cover these places by arrangements with nearby academic-based children's hospitals.
The list you guys have going looks pretty good. From residency, I did know of one OMFS guy who specialized on children and worked at the Children's Hospital--so it apparently is possible. There are also some pediatric surgeons who specialize in "trauma," but at most children's hospitals, trauma isn't nearly as big and doesn't receive nearly the focus as it does at an adult trauma center. Most pediatric cardiac surgeons specialize exclusively on children (including cardiac and pulmonary transplants), but as has been pointed out, I think options to be a liver transplant surgeon and do only kids are more limited--because of the lesser demand for such surgeries. There are definitely pediatric-only ophthalmologists, urologists, orthopedists, general surgeons, neurosurgeons, ENTs, and plastic surgeons. Agreed that I don't recall seeing any vascular surgeons who do only pediatrics. And I think most of the surg-onc work for kids is done by general surgeons who do fellowships in pediatric surgery. Also have never heard of a "pediatric" OBGYN who does gynecologic congenital work and other such things--but they may exist somewhere in the more specialized children's hospitals.
In any event...the takeaway is that if working 100% with kids is your career goal, realize that you will most likely have to live in a city with a dedicated children's hospital--and that you may have to move somewhere you weren't really considering for your first job because these jobs only open up periodically due to their limited nature.