Hi Mare
Having now found the Aner COOK / Charlotte SMART marriage, I get the feeling that William Robert COOK was perhaps born, Brighton, ENGLAND ?
Some "online" activities for you : -
1) Certainly contact the person who has posted the COOK / COOKE BDM info ~ there may just be a link to your family ?
2) William Robert COOK ~ "possibly Superintendent of Napier Prison" ... this job sounds like the pinnacle of a career .... perhaps William retired in Napier ?
(a) Check for a burial in Napier
http://freepages.genealogy.rootsweb.com/~shipstonz/cemeteries.html
(see Napier City Council link)
(b) Napier Library may have information about the Prison and its employees ?
3) UK Census - post "look-ups" at RootsChat UK
(keep the details brief ... good idea to have a look first to see how others have worded their enquiries) :
> 1841 - you may find Aner COOK ?
> 1851 / 1861 /1871 - search for Aner, Charlotte and family.
Good luck ... we look forward to learning what you've discovered.

Lu