You can apply to live in New Zealand permanently if you have a child who is a New Zealand citizen or resident. You will also need to meet INZ (Immigration New Zealand) income and investment requirements.
Invest in New Zealand
You must keep at least NZ $1 million invested in an acceptable investment in New Zealand for 4 years.
INZ ask for evidence you have kept your funds invested at the end of the second and fourth years you are in New Zealand. You will have 3 months to provide the evidence. It is OK to transfer funds between acceptable investments.
If you already have funds in an acceptable investment in New Zealand when you apply for residence, INZ can start your investment period from the time they approve your application in principle.