Information on the best vow/Baare to do for a child's health and safety
Try doing a Bodhipuja at Sri Nagavihara temple, Kotte. It seems to help some people. I'm sure there are many other places that work too. Ruwanveli Saya, Sri Maha Bodhiya, Dalada Maligawa are obviously the best places you can try. 

As a Buddhist you should make the vow to the Buddha, with virtuous gods(all who supports the Sasana) as witnesses. A good vow would be "if the child lives, we will offer him to the Sasana" 

If your child can speak the language, teach him/her the "iti pi so bhagava araham..." verses with meanings and tell to chant regularly in his mind while contemplating the meanings. 

Also, if you have money, free some animals in slaughter houses and wish for your child's health.