It’s usually pretty easy. He could just make an appointment online for US passport services in NZ. The US CG in AKL has plenty of availability for most Monday and Wednesday mornings in the late summer/early fall down there. And if the person were to need the expiring US passport back during the stay in NZ, the USFS staff there can even manage to return the US passport for use by the applicant until the renewal passport comes back into ACS at the US CG there.