I have used Royale Shuttles to get from the airport to down town Chirstchurch and they are the best. For 2 of us it cost $20NZ right to the door of our backpackers, and the next day we went to the railway station and it cost us just $5NZ each.
The guys were great and helped us with local knowledge.
Their ph: +64 3 341 810 and their web:
www.royale-pt.co.nz