Have you tried looking at the property sections on the online newspapers for Wellie area?

I think it's a fact that a lot of NZ rental properties come unfurnished, so you may have a job finding one. You never know though, you might get lucky.

This is a link to a list of NZ newspapers , but you may need to download a cookie before you can read them. Click on a paper and it'll take you to a page that explains what to do.