This is not my area of expertise but this came up in a conversation I was having with a lawyer yesterday so I will give you my two cents (which is just based purely on gossip!)...
While there is no obvious restriction on your student visa about being self employed however - when you go to apply for a work visa or residency they will ask if you have been working in NZ before. If you answer yes - as "self-employed" then probably your application will be declined (because you are on a student visa - not a self-employed visa).
You must be upfront and honest with your declarations with immigration. If they ever get a sniff of you misleading them then all future visas for NZ will be in doubt.
Check out the Study to Work Visas mentioned in the other post. Get yourself a job that is on the shortlist -
http://skillshortages.immigration.govt.nz/