Hire a single wheel or two wheel cycle trailer for your tour of the South Island. Hire one for $100 a month or buy one for $300 and I can buy it back from you (typically $150 in reasonable condition). Courier back to Christchurch can be arranged for $50 as long as your last accommodation is ok having the pickup from their place.
You can try a two-wheel trailer for free for a month if you are thinking of buying one and want to see what its like. Pickups and usage must be in Christchurch.