While this may be an open question, I don't believe it is illegal. However, it opens the Guardian up to potential problems if anyone witnesses the spanking and reports it to Child Protective Services. I respectfully suggest you refrain from spanking, but that is a personal opinion, not a professional one.
Of course, you can always call Child Protective Services and ask them, but I suspect you'll be told it is illegal and if they already get your name, well, you know the rest.
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This answer does not form an attorney/client relationship with anyone and any answers do not constitute direct legal advice and should not be followed unless and until you have spoken with an attorney of your choice.
Understand that there is a difference between something being illegal, and something that may threaten the health, safety and welfare of children. And while it may be difficult in this day and age to say whether or not a spanking is or is not legal, if you are worried about the health, safety, or welfare of a child or children, there are people that you should talk to immediately.
A lot will depend on context in a case like this. Are the spankings very frequent? Are the spankings tied to some act of the child that other parents who do spank their children would agree is an appropriate act for which to spank a child? Has this guardian ever been in trouble with the pollice or child protective services for family or criminal issues? Has someone else ever suggested to him that they are uncomfortable about the children being spanked?
Posting on a message board often leaves the lawyers with more questions than answers - if you have reason to be concerned about the safety of a child or children that you know, you should immediately the police or child protective services. Below please find links to the Office of Children and Family Services and a guide to the Child Protective Services system. Lots of luck to you.
Mr. Reimer is licensed to practice law in NJ and NY. His response here is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. Mr. Reimer strongly advises the questioner to confer with an attorney in their own state to acquire more information about this issue.