When your baby is borned, the hospital will ask you if you have a pediatrician for the baby. If you answer "no", they will assign the on-duty pediatrician to you temporarily while you are in hospital.
When you leave the hospital, you can contact the same pediatrician. Someone told me before that they cannot refuse to see your baby within the first some days if they have seen the baby before in hospital, and you may be able to ask the pediatrician to accept your baby.
Otherwise, you can also ask the hospital for a list of pediatricians who are accepting new patients, but their list is usually out of date and when you call, the pediatrician may also refuse.