Thanks Bren.

Hello Donut
Since the time of your last enquiry, we're happy to be able to tell you that some advances have been made with our NZ BDM records ... and you are now able to search for a great many historical records, online.
http://bdmhistoricalrecords.indentityservices.govt.nz/home/Here's an example of births of children listed for a "Harriett and Joseph COOPER" (who very possibly are, who you may be seeking ?).
Births1900 - Daphne Hellen COOPER
1901 - Ida Marjorie COOPER and Jean Mary COOPER
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... and listed for "a Harriet (spelt with just the one "t") and Joseph COOPER, are
1898 - Laurence Joseph COOPER
1896 - Genevieve Eileen COOPER
1895 - Nora Isabel COOPER
... so these too, may be children of the same Harriett and Joseph who married in 1894 ?
Armed with this information, you can then take a look for marriage records (currently available online, up to 1928), for these COOPERS.
[Wise also to check the death index, as some of these children may have died in infancy or remained unmarried].
Once you've sorted out some "possibilities", then check the Archives NZ website (link in the Resources section of this board). Often names and locations of people can be found there, if for example their wills have been probated or they've been involved in other transactions recorded by a government department.
Happy hunting !

Lu