Let me put it this way: Teachers are highly sought after in New Zealand, but certain boxes need to be ticked. Home schooling is very common, and the arts are respected. The diploma in software programming would give you one great option though: The NZ government currently extends training offers to all who have some sort of tertiary qualification. Within about one year of additional training in New Zealand, you could have full qualifications to be a teacher - and considering your diploma is in software programming, you would make a very plausible IT teacher, which is on the skills shortage list, and carries something very close to a job guarantee.
You would need to come in on an open work visa first, establish yourself in a place, and start that process.
Unlike other immigration countries, NZ allows status changes to your paperwork while you are here. Work with an NZ immigration worker at a consulate or embassy to find out more, you’ll be surprised how helpful and friendly they are, and you’ll see your plan is quite feasible. Teachers are extremely in demand.