Hi Lilian
Airport passenger lists for that period are patchy - one of the problems is that flights did not arrive (or go) direct NZ-England. Travellers would often stop over in Singapore, Australia, Fiji, etc for some days before travelling on. Consequently they appear as travellers from those airports. Can you provide a tighter time frame to check - as this material hasn't been indexed.
I presume you're not in NZ?? If you are, most metropolitan libraries have a copy of the BDM microfiche up to 1990. Otherwise give us some details of the names of the child and the mother and we can check the relevant years and give you an answer.
If you contact the BDM Central Registry they'll charge a fee for each year searched whether successful or not. When you do apply for a 'printout' make sure you ask for the $20 version (NOT a certificate which costs more and has less info!).
Elli