Thanks, that's the site I was looking for. Based on what I'm seeing there, it's not a good idea to have anyone else transport valuables for you, because they need to declare (and probably pay duty for??) anything that's not their own personal effects, even "gifts."
I don't see anything specific about time frame for bringing in your own stuff as a migrant, but I'm guessing it's the first time we travel to NZ with a residence visa. So I might have our relatives keep the heavy coin collection until the next time we visit them, then we could transport it ourselves in checked luggage (provided it's our first time re-entering NZ as migrants, I guess?). I'll have to check the weight limit for checked luggage, haha...
Or I could risk it and just put it in the container. Some other stuff in the container is irreplaceable, too - so the risk isn't much different. I guess it's just the sentimental value that makes me hesitate.