Go through your results for flights to Palmerston North in New Zealand with Netflights. Although Singapore Airlines usually has the best prices, it's best to double check what's available for your travel dates.
If these flights are too expensive, try searching for a different time of year. So if your dates are flexible, consider looking at different times of year.
But if you're struggling to find flights to Palmerston North that work for you, try looking at other airports in New Zealand.
Looking at a few different departure airports will give you even more choice. See what you can find. And remember, it's best to book your flights in advance wherever possible.