This website is not designed for people to have attorneys do free legal research for your and get back to you with a report. You will need to hire an attorney for that purpose.
From your brief description, it sounds as if your situation has two parts: (a) finding an attorney who knows and understands the law in this area and what precedent there is for compelling payment for private school; and (b) having an expert witness to report, discuss and/or opine on educational issues generally and as they relate specifically to your child's needs. An attorney can submit a memorandum of the law, but a court generally requires a report or testimony from an expert if they are considering issues beyond the law.
* This information is general legal information and is not intended to be advice on your particular case.
Many attorneys feel (myself included) that we cannot "ghost-write" a brief, and then have you sign off on it. Either the attorney would need to be hired for the case, or you would need to do the research yourself. If you need it for some other purpose, that's another thing. Thus, you're encouraged to schedule a consultation with a NYC Child Support lawyer to explore the issue further.
* If you found my answer to be helpful, or the "best answer," please feel free to mark it accordingly.
Schedule an appointment with an experienced family law attorney. Also, you will need an expert to evaluate your child to determine if he is a special needs child.
If this answer is helpful, then please mark the helpful button. If this is the best answer, then please indicate it. Thanks. For further information you should see an attorney and discuss the matter completely. If you are in the New York City area, then you can reach me during normal business hours at 718 329 9500 or www.mynewyorkcitylawyer.com.
What you need is a consultation with NY Matrimonial attorney
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: email@example.com; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.