None of which I'm aware. Dutchess County's private/parochial school listing doesn't name any, aside from Astor Learning Center, which is geared towards children with special needs.
There are plenty of private schools further south in Dutchess County. For example, there are some exclusive schools like Millbrook (in Millbrook, clearly) and Catholic schools like Our Lady of Lourdes HS, Holy Trinity, and St. Martin's in Poughkeepsie, to name a few.
I have known people from the Rhinebeck area (Staatsburg) who went to private school in Poughkeepsie because that was their closest, best option.
