Hi luiza13,
100k is correct, children born after 1st January 2006 don't automatically gain citizenship by birth, you can find some more information on this
here. This is an important point as JandM has pointed out and one you need to check. Children born in NZ after this take on the same status as their parent.
I thought I might be able to add something to this thread as I have recently been working on a case that was very similar - a family on the verge of being deported came to me for help to see if there was any way they could stay as they had a child who is an NZ citizen. I pulled the case apart, talked to the immigration department's compliance staff and completed quite a bit of research as this is a complex area affected by NZ and international law (for example the United Nations Convention on the Rights of the Child which NZ has ratified).
If you do want to fight this I suggest you contact a specialist lawyer or immigration adviser quickly before deportation action is taken (that's not an advert, I wouldn't be able to to help as I am fully committed on other cases already right now) You need the whole situation assessed including the information held by the immigration department (one of the first things to do is to get a copy of the entire INZ file under the Official Information Act to understand what has happened) to obtain clear advice.
You may be surprised at what is considered important and what is not. Understanding everything which might affect the case will give your brother's family the ability to make an informed choice about whether this is something which can be fought. Important points for example include which country the child might need to go to (affecting their well-being, access to education etc.), what has happened (for example how long your brother has been unlawful) and whether a deportation order has been served on the parents yet (this makes a big change on what you can do and how you should do it).
While the rights of the child are important they do not block the immigration department from deporting parents in situations like this unless there are true humanitarian grounds - something which is quite rare. Understanding your rights and the deportation process can help a lot, as can having a strong advocate actually dealing with the immigration staff to ensure your brother's family gets a fair go.
Hope that's a help.
Mike
Migrant advocate | licensed immigration adviser