unfortunatly, the Southerner does not run anymore, in Febr. 2002 it had its last journey from Picton to Invercargill....have a look at the intro map...that long beautiful stretch, mostly along the South Island coast, is fallen to coast cuttings by Trainsrail...these days they call themselfs TOLL
My Journey from Invercargil to Christchurch is a very memorable one...took around 8h..and Timaru had the best, NZ Railwaystation Tearoom I've ever been in.
As Timaru is not all that big, you can probably get around on your own two feet in the central city. A car would be very usefull if you intend to see a bit more of the region. There are four bus routes that travel from the main street area out to the suburbs, there are plenty of Taxi companys avalible, try Budget Cabs for friendly cheap service.