There are a number of visa options for parents of New Zealand residents or citizens to help them join their family in New Zealand. If your child is a student in New Zealand, you might qualify for a Guardian of a Student Visitor Visa. A subsequent application for a variety of conditions might even allow you to work while your child is studying in New Zealand.
There are a few options for parents of New Zealand residents or citizens to help them join their family permanently or temporarily. They all require that you have a child or grandchild that is a New Zealand resident or citizen, and some require that you be sponsored by them or their parents (if you are a grandparent).