I would recommend that you use printouts, image of a hand written record, rather than certificates, which is a transcription.
I think there are additional births / death for children born to Annie -
BDM NZ births
1880/9809 COOK John Edwin parents Annie / George
1881/3099 COOK Lena Gertrude parents Annie / George
1883/6858 COOK Jane Elizabeth parents Annie / George
1884/4515 COOK Percy Harry Potter parents Annie / NR
1885/6454 COOK Alice Constance parents Annie /NR
1888/2059 COOK Ethel Annie parents Annie / NR
1890/6403 COOK Lois Hilda parents Annie / NR
1892/6450 COOK Dora parents Annie / NR
BDM NZ deaths
1883/1564 GARDNER Catherine 6W
1884/4549 COOK Percy Harry Potter 7M
1886/1494 GARDENER Alice Constance 9M
1891/1226 COOK Lois Hilda 10M
1893/3753 GARDNER Dora 17M
GARDNER Dora 17 yrs bur. 17 Jul 1893 Public Plot 272 Record #30644
Burials Bolton Street
GARDNER Catherine bur. 14 Mar 1883 C of E Plot unknown Record #96382
GARDNER Alice Constance bur. 12 Feb 1886 Public Plot 63b Record #96381
GARDNER Louisa Helda bur. 17 Feb 1891 Public Plot 63b Record #96385
The Land Transfer Office in Wellington might be able to give you the history of any land in Webb Street which was owned by Annie COOK or George GARDNER. Previous and later owners might lead to relatives.
It will be interesting to see what is on the marriage certificate.
There is a Primitive Methodist church in Webb Street. I think the church united with Methodist Church in early 20th century. Methodists had baptism. Records for the Webb Street church would be useful to find.http://www.myprimitivemethodists.org.uk/page/primitive_metho...
The Archivist Methodist Church of New Zealand Archives
PO Box 931 Christchurch New Zealand 8140
Phone 03 366 6049