Qatar Airways + Etihad are offering some cheapish flights to Europe for travel between February & April 2017. The next best fares are about $300 more and involves flying China Southern. Qatar Airways is the #2 best airline in the world and Etihad is #6 according to Skytrax. (Air NZ is #17).
I've linked to Momondo as Skyscanner wasn't showing much.
Travel dates:
February – June 2017
Sample dates (Auckland – Pisa – Auckland):
Feb 8-15, 9-18, 12-19
Mar 1-8, 9-18, 16-25
Apr 2-9, 9-16, 23-30
May 4-13, 7-14, 14-21, 18-27, 21-28
Jun 1-10, 4-11, 5-12, 6-13, 7-14, 8-17, 11-18, 12-19, 13-20
Routing:
Auckland – Venice – Auckland
Wellington – Venice – Wellington
Christchurch – Venice – Christchurch
Auckland – Rome – Auckland
Wellington – Rome – Wellington
Christchurch – Rome – Christchurch
Auckland – Pisa – Auckland
Wellington – Pisa – Wellington
Christchurch – Pisa – Christchurch
Auckland – Milan – Auckland
Wellington – Milan – Wellington
Christchurch – Milan – Christchurch
For the Etihad flights, have a try booking via Etihad's site with the current coupon codes. I wasn't able to select return flights but maybe you can do a multi-trip involving one-way flights.
Via Fly4Free