While working on a client's research today, I found these fabulous lists of the men aged between 18 and 60 years living in the Christchurch area and who were "liable to serve as Militiamen for the year 1860-61 in the Militia District of Christchurch" in Papers Past.
It's important to remember that this is a list of those "liable to serve", it doesn't mean that they served.
You can find the lists here:
Lyttelton Times, 6 June 1860 - Abbott to Edwards (James)
Maybe you'll find some of your family here.
EDIT: Here's a link to the Militia Act 1858, that gives more explanation of who was liable and what was required.
If you do have family in Christchurch, have you checked out the Canterbury Church Register transcripts in Tūranga, Christchurch City Libraries?
Can't get to Christchurch to research? Contact us.