Hi, the NZ BMD only shows two James Reids dying in 1903...
1903/4770 Reid James 58Y
1903/6794 Reid James 85Y
...so assuming that he is one of these he would have been born in either 1845 or 1818.
I can't find any marriage or definitive children's births in the NZ BMD and checking newspapers at the national library (http://paperspast.natlib.govt.nz/
) hasn't helped but you may have more luck searching for other events related to the family.
James Reid (European) married Ripeka Matuatonga (full Maori).
Children from this union were:
(Papu) Robert John Reid, alias Papu Te Huatu or Huetu
Hoani, alias John Reid
William Matuatonga, alias William Reid or Riri Te Huetu or Huatu.
The website gives a contact (beverleyreid(at)paradise(dot)net(dot)nz) for someone with knowledge of this family.
I think your best course of action is to try to tie down James' immigration but without knowing a decade, at least, such a common name makes it tough.