Mary Amanda Demarest married Thomas Haskell Wood in New Orleans in 1845, when she was 14 years old. Cousin Larry, our Wood family genealogist, has records of her marriage, her children, and her burial, but Mary Amanda's exact birthplace and date -- and her parents -- remain a mystery. She seems to have been born in New York City in 1831 (according to death cert, etc).
Last month, at cousin Larry's suggestion, I checked the records of the Reformed Dutch Church of Greenwich, New York City, where many Demarests were members. Alas, no Mary Amanda. But there were these three records of children adopted by Mary Van Orden Demarest, as you can see from the above excerpts from transcribed church ledgers.
This discovery has led to a new line of thinking: Maybe Mary Amanda was adopted into the Demarest family? Her birth record wouldn't show up as Mary Amanda Demarest. Of course this is only a theory. More research is in our future!
2022 update: No progress after all these years. The parents of Mary Amanda Demarest are still not proven.