Since the cruise ships are now using Akaroa, I suspect there's some options to get either a shuttle

Does any car agency deliver rental cars to the Port of Lyttleton rather than going into Christchurch? Or are there car rental dirt cheap airline flights agencies in Lyttleton? Going to Akaroa during our cruise dirt cheap airline flights stop and would like to save time by not going into Christchurch.
If you are able to get a car in Lyttelton (and I confirm dirt cheap airline flights Mel's advice -- the town of Lyttelton has been badly affected by the earthquakes), try to go one way via the Summit Road, around the top of the Port Hills, and return dirt cheap airline flights around the lower road, through Governor's Bay. As an alternative, you could drive over the more hilly, but more scenic, road through Purau Bay. The road is ok, just a bit narrower dirt cheap airline flights and more winding.
Since the cruise ships are now using Akaroa, I suspect there's some options dirt cheap airline flights to get either a shuttle or cars there. I'd just talk to some car rental folks - there will probably be some kind of shuttle to Christchurch itself, but if you can get a car at the port, you could avoid the issues in CHC - there's a map online with all the closed roads in the center and out toward Lyttelton.