Hi Michele,
I would expect the only option open to you would be the Long Term Business Visa. The only drawback to this is that you have to benefit the NZ economy in some way, which usually involves employing 2 or 3 people. It's also quite an expensive and complicated route. I doubt that websites (if thats the only way the business operates) would be acceptable, but I really couldnt say for sure.

What category did you originally intend to go by?