We have Fijian birth, death and marriage records on microfilm on permanent loan from the LDS in the Central Auckland Research Centre. They are divided into the categories General, Fijian, Indian and European and are helpfully indexed.
This is an example of an index, taken from Fiji births, general index 1876-1960.
A birth record may give you date, name, sex, parent’s names and ages, whether married, previous children, profession and parents’ birth place, with signature or their ‘mark’. This example is from Births general 1883-1891.
This example is from Births general 1911 in Fiji (although the child was born in 1888 the birth wasn't registered until later, along with two of his other siblings).