That would depend where the kids are born. If you are residing in NZ at te time, they are automatic kiwi citizens, so there is no problem at all. If they are born outside of NZ, you would have to sponsor them, although to what degree I dont really know.

If you cannot sponsor your partner, then he will most certainly have to find his own way in. Without a job, he has the option of a Working Holiday Visa if he is aged 18 - 30, or else it will just have to be a visitors permit, until he can a job.