Tony said "More information can be found if you order their certificates (cost about $20)."
Please do NOT order the legal certificate for family history purposes; you WILL be disappointed. Get the printout - I explain why at http://archiver.rootsweb.ancestry.com/th/read/NEW-ZEALAND/20...
The web site you need for this is BDM Online - Historical Records (https://www.bdmhistoricalrecords.dia.govt.nz/Home/
If you don't want to order online, or are dealing with more recent events that aren't on the historical site and don't have an iGovt registration, you can order via ordinary mail - go to Births, Deaths & Marriages (BDM, http://www.bdm.govt.nz/
), click on the button "Births", then click on the link "Obtain application forms and fin the associated fees", then "Birth, Death, Marriage, Civil Union or Name Change certificate or printout", then "Request for Birth Certificate or Printout BDM 93B". Print this form, complete it with what you know, and send it off with your payment. I've also been told you can call them and order over the phone.
If you are a member of the New Zealand Society of Genealogists (NZSG, http://www.genealogy.org.nz/
) enquire at their Certificates Collection before making purchases at BDM. If they're holding what you're looking for, it is much cheaper.
"3 Feb 1891 Star Newspaper has the heading Serious Accident at Cust. Daughter of Henry Dunlop was run over by a traction engine's straw elevator and wasn't expected to live.
24 Sep 1921 Miss Eva Dunlop was a bridemaid at a wedding at the Knox Church in Lower Hutt."
I'm guessing, but I'd say these came from PapersPast (http://paperspast.natlib.govt.nz/
). It's a great resource.
You may also find Archway (http://archway.archives.govt.nz/
), the online index for Archives New Zealand (http://www.archives.govt.nz/
It's free to walk into the office holding a file of interest to you and view it, assuming there are no restrictions (which are spelled out in the Archway listing if there are any). If you can't go yourself, a friend can visit on your behalf (barring any restrictions as above, or where permission is given to a specific person, of course) and take photos. Ask here if you need help, someone might be able to visit for you.
Hope this helps. :-)