The New York Times has an interesting piece on nanny pay in Brooklyn:
http://cityroom.blogs.nytimes.com/2011/11/02/a-look-at-how-brooklyn-nannies-are-paid/
The advice of Susan Collins is right on: “[T]he best thing to do for all parties is to pay your nanny on the books (and it’s the law).”
So hire a good accountant or nanny tax payroll company, and pay your taxes! Also, be sure to have a great nanny contract in place to cover all the other important issues of nanny care.