Do you know where Bentley is/was? I don't recognise the name, can't find it on a map, and it's not in my 1952 NZ Guide. The Kaipara Harbour is a very large body of water, with a huge coastline.
What are you calling "late 1800's"? Can you be more specific?
It might be that you're dealing with a spelling variation on LEWIS, which means it could be difficult to find the right entries at BDM Online - Historical Records (https://www.bdmhistoricalrecords.dia.govt.nz/Home/
) as it only deals with exact spellings.
You may have more success looking at the older microfiche indexes, where you can see a whole page of entries at a time, so variations on LEWIS would be easier to find. You'll find the fiche in libraries and genealogy groups around the country, and if you're a member of the New Zealand Society of Genealogists (NZSG, http://www.genealogy.org.nz/
) you can use their Research Service to have an NZSG volunteer look up their copies for you, for free.
Then, of course, some births were never officially recorded. :-(
Hope this helps. :-)