There seems to be a couple of issues here. First and foremost, your child has to be residing in the USA. If he's gone more than 6 months, he may require a reentry permit. I would highly recommend you bring him back to the USA ASAP so as not to violate the terms and conditions of his green card.
Once you have your oath ceremony, your son should be able to get a US passport if you either have court ordered documentation granting you full custody or you have permission from the other parent to get his US passport. The initial passport appointment requires you, the other parent (unless circumstances listed are met) and your child to appear at either the post office or the passport office.
IMO, there is no way for him to obtain the passport abroad because the circumstances by which it would be granted are not met. I'd be concerned that the consulate or embassy would deny because the child does not appear to be living in the US and has no reentry permit.