http://www.immigration.govt.nz/migra...tvisas/#family
Partners and children of students
If your partner or children want to come to New Zealand with you, they need to apply for a visitor visa or, if they will also be studying, their own student visa.
New Zealand Aid Programme (NZAP) Students
Partners of NZAP students may be eligible for a work visa valid for the duration of their partner's NZAP scholarship. Dependent children may be eligible for a student visa.
OR ELSE
http://www.immigration.govt.nz/migra...am.htm#student you could sponsor your partner for a partner-sponsored temporary work visa.
Your partner holds a New Zealand student visa
You must be in a genuine and stable relationship with your partner and they must hold a New Zealand student visa to study for:
a level seven (or higher) qualification on the New Zealand Qualification Framework in an area of absolute skill shortage as specified in the Long Term Skill Shortage List, or
a postgraduate qualification.
In that case, your child would need a visitor's visa (application linked to your wife's with a covering letter, so it will match hers and yours for length of time) if s/he is under five years old, or a student visa if five or older.
These last visas are the ones they can get for after your course - the post-study work visa is a work visa, so you will still be eligible to sponsor.