Can I (custodial parent) file to terminate child support and a very large debt in arrears if we make a private agreement?

I have seen your question. My name is David Salvaggio.  I head a law firm that devotes its practice exclusively to New Jersey Family Law matters, including child custody and child support.  It's all we do. Unfortunately, a good Family lawyer will need more information, before being able to try to answer your question. To obtain further guidance, I recommend that you meet as soon as possible with a very experienced lawyer who devotes his/her practice exclusively to New Jersey Family Law matters such as yours.  Go over your situation in detail with the attorney, get educated answers to your questions, and obtain expert guidance as to the best course of action. In my opinion, it will be well worth the cost of the meeting. Your question does not specify the town in which you live.  My firm's offices are located in Morristown, NJ (Morris County).  We handle cases in all of the counties in northern and central New Jersey.  Please feel free to take a look at our Firm Website (www.salvaggiolaw.com) for further information.