How can a green card holder bring newborn legally to USA?

If a child is born to a permanent resident overseas, the child is eligible to enter the United States without any visa (or for that matter any paperwork at all) if he or she travels before the second birthday along with any of the parents and it is their first trip back to the US after birth.  The kid becomes a permanent resident immediately if legally admitted by a border agent.  For the process to go smoothly, the child should have a passport, a birth certificate (with an acceptable translation if not in English), and the accompanying parent must have valid green card (Form I-551) or reentry permit (USCIS Form I327)

Since there are uninformed airline or customs agent in every country who will have a fit to see a baby without a visa, it is better to have all your paperwork in order and allow extra time to board the flight in case there are delays.  If the low level staff gives you a hard time, insist on speaking to a supervisor.  On arrival in the United States, the process will be more straightforward as long as you have all your documents in order.  Remember that if all of the requirements are not met, the child can still travel to the US but the process is more cumbersome.