I think the best thing to do would be to look at your itinerary and then Google "churches", "Christian groups", "... (your) denomination or faith group" in areas where you will be staying at that time. We've got the internet like everybody else these days.
So for arguments sake, assuming you're in the Baptist church (I have no idea what group you're in) and if you know you'll be in Sydney from 13-16 October, google "Baptist Churches in Sydney". You may wish to be a bit more specific if you know the address of the accommodation you'll be staying in eg. Kings Cross (a bit of a joke there - it used to have a reputation as a red light district).
I googled "Churches in Kings Cross, Sydney, Australia" and came up with
https://www.google.com.au/search?rl.......0...1.1.64.psy-ab..0.0.0....0.ynJ8OMblYEI
Amongst the results were the Wayside Chapel, St. Canice Catholic Church and the Hope Sydney Church.
I'm assuming you'll be moving around a bit, so you'll only have a number of short periods in each location. Which means you will need to do a bit of planning beforehand based on location.
I live well to the north in Queensland, so I can't help with local knowledge of Sydney, Melbourne or New Zealand. You'll just have to do a bit of research, and the internet would be the easiest way to do it.
All the best, and I hope you enjoy your trip.