baikal3, I believe you are giving wrong advice. One can apply for N-600 to obtain proof of citizenship in the form of a certificate of citizenship. However, the citizenship was acquired at the time the parents took the oath (if all other requirements are met, under 18 years of age, physical/legal custody of child and having a GC). Passports are issued just with child birth certificate, child's Green Card and parent naturalization certificate. You don't need to obtain a certificate of citizenship for the child before you can apply for a passport for that child. Please take a look around the forum for references to CCA or Child Citizenship act.
Going back. I don't see anything baikal3 has said that is actually true Wrong on documents to obtain passport for child. Wrong on when the child becomes a citizen and wrong again on needing a N-600 for the child to become a citizen.
Going back to the original question, it is possible the child can travel on GC although the child is already a US citizen. However, that wouldn't be the right thing to do. For this to work the Indian authorities have to believe the Indian passport is still good, and that the child's GC is good. Unless they know the intricacies of US immigration law and figure out the child is already a US citizen they should let the child board. The US immigration authorities might figure out the kid is a citizen already, but they might accept the GC as proof of identity and indirectly of citizenship. I don't know. I haven't tried this and I am not sure if it would actually work, but it might work.
Going back. I don't see anything baikal3 has said that is actually true Wrong on documents to obtain passport for child. Wrong on when the child becomes a citizen and wrong again on needing a N-600 for the child to become a citizen.
Going back to the original question, it is possible the child can travel on GC although the child is already a US citizen. However, that wouldn't be the right thing to do. For this to work the Indian authorities have to believe the Indian passport is still good, and that the child's GC is good. Unless they know the intricacies of US immigration law and figure out the child is already a US citizen they should let the child board. The US immigration authorities might figure out the kid is a citizen already, but they might accept the GC as proof of identity and indirectly of citizenship. I don't know. I haven't tried this and I am not sure if it would actually work, but it might work.