Born 1914 Male 
Hello....
Just wondering how accurate your source is regarding 1914. I only ask because according to the BDM NZ website several of the birth years you've mentioned are off by a year or two (see below). Maybe 1914 is off too.
the children may have all been born in Auckland.
I checked the BDM Births fiche for four of the children and their births were all registered in Auckland.
Couldn't check them all sorry as I was short for time.
There is only one male DYER birth registered in Auckland in 1914. I can't post his BDM Births details on the board (because of the 100 year rule) but I can post his BDM Deaths details (because of the 80 year rule). The
BDM website registration number is 1984/34551
He's listed on the
Waikumete Cemetery website. His death notice is mentioned in the Seton Kellaway Collection. Maybe you can ask for a look-up to see if any siblings are mentioned.
There is also only one male DWYER birth registered in Auckland in 1914. Again I can't post his BDM Births details (because of the 100 year rule). I also can't find a record in the usual places for his death. But if you want the BDM Births fiche details it's no problem to PM them to you.
born c1888 male?
I looked one year either side of 1888 for Auckland births. There didn't seem to be any DWYER's. There were a few DYER's.
1887/3479 Walter Edwin DYER and Ruby Gordon DYER (twins?)
1888/139 Bertie DYER
1889 - No males
Here are the BDM website listings I mentioned earlier, some of which disagree with your source.
Esther Eliza 1890
BDM NZ 1890/12905 DYER, Esther Eliza - child of Esther and Frederick Henry
Norman 1892
born 30 Mar 1893
BDM NZ 1893/5775 DWYER, Norman - child of Esther and Frederick Henry
Hilda 1895
BDM NZ 1895/18654 DWYER, Hilda - child of Esther and Frederick Henry
Victor Frederick 1901
born 28 Oct 1899
BDM NZ 1899/18135 DWYER, Victor Frederick - child of Esther and Frederick Henry
Henry 1903
born 2 Dec 1901
BDM NZ 1902/663 DYER, Henry - child of Esther and Frederick Henry
Hazel 1904
born 12 Nov 1906
BDM NZ 1906/18164 DYER, Hazel - child of Esther and Frederick Henry
Frederick Henry 1905
born 8 Jun 1904
BDM NZ 1904/3999 DYER, Frederick Henry - child of Esther and Frederick Henry
Linda Isabella 1911
born 25 Mar 1910
BDM NZ 1910/7167 DYER, Linda Isabella - child of Esther and Frederick Henry
Regards
Beg