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 Immigration New Zealand's income and investment requirements.
You must meet health and character requirements
Your child must be a New Zealand citizen or resident and you must be the parent or legal guardian of your child
Your child must live in New Zealand
You must have no dependent children
You must have $1 million NZD of lawfully acquired funds to invest in New Zealand for four years and transfer those funds to New Zealand
You must have $500,000 NZD of settlement funds
You must have annual income of at least $60,000 NZD
You may include your partner in your application if they meet the requirements for residence
You must invest your investment funds in acceptable investments for 4 years