While delving into my paternal grandmother's family history, I found a family tree on Ancestry, with all the usual caveats about Ancestry family trees, that suggests that her great grandmother, Margaret McMaster gave birth to twin illegitimate sons in 1857, before she married Thomas Hunter in 1860. In this case the information is backed up by an image of what appears to be the parish register of baptisms, which states the father's name, James Galbraith, the twins' date of birth which was 27 September 1857, and the baptism date which was 15 April 1858. Margaret's address is given as Saddle Hill, which fits with where the McMaster family were living at the time. I can also find a record of the baptisms of a James and John Galbraith in 1858 for the East Taieri parish in the Presbyterian Research Centre's baptism indexes which fits with the image.
What I am struggling with, however, is finding any formal record of their birth registrations on the Births, Deaths and Marriages Online website in New Zealand, under either the surnames McMaster or Galbraith. I am assuming that the registration of births was a statutory requirement by the time of their births, which means that their births should have been registered. While the baptism record gives their surname as Galbraith, they seem to have both been known by the surname of McMaster for the duration of their lives.