Hello Elan,
I normally try to post helpful advice but I've certainly stuffed up on this thread. For some reason I got stuck on the Ellesmere Cemetery burial when you clearly said Geraldine Cemetery in your earlier reply. Sincere apologies.
And your post didn't sound rude at all. To be honest, if you hadn't mentioned it, it would never have crossed my mind.
All I was trying to say was don't take as gospel everything you read on a BDM NZ certificate (which I guess also means the BDM NZ website and the BDM NZ fiches).
And I guess the same goes for parish registers.
Speaking of which, do you know if the 1904 marriage was in a church. If so, have you checked the baptism registers for the 1904-05 birth.
Pretty straightforward if they were Catholic. Just start a request thread for a look-up of the "Catholic Diocese of Christchurch Baptism Index CD - 1840 to 1908".
I'm off to the library this afternoon so will check the Births fiche for a 1904-05 Christchurch-based male COOKE birth. Hopefully there aren't too many.
EDIT:Back from the library :-)
The only 1904-05 male COOKE birth which appears on the Births fiche but not on the BDM NZ website is one Harry COOKE 1905/2283
The birth was registered in Christchurch in the second quarter (Apr-Jun) of 1905.
Might be worth looking at BDM NZ Deaths - 1974/32352 COOKE, Harry - d.o.b 9 March 1905 - d.o.d 1 Jan 1974 - buried at Wakapuaka Cemetery, Nelson
Nelson Cemetery database
http://www.nelsoncitycouncil.co.nz/cemeteries-database-2/1974 Probate for a Harry COOKE (May or may not be relevant)
COOKE Harry - Christchurch - Railway Servant 1974
http://archway.archives.govt.nz/ViewFullItem.do?code=21802245ANOTHER EDIT:I've just re-read the thread and have realized that, although you didn't mention it, you seem to already know the identities of the four children.
And you clearly stated in your original post that you wanted info on Martha, not the children, so I've been on a bit of a wild goose chase.
Sorry about that. Will step back for a day or two :-)
Regards
Beg