Hi Carole ... I am trudging through a lot of varied information on the Nightingale family and finding many variations on names and dates. Unfortunately, I am unable to help you with your search for Mary's parents. (I had also come across the name Mary Capen (alt Capon) as a wife for William so I am researching both avenues.)
However, if my preliminary sources and searches are correct, Mary's "William Nightingale" would have been my 5th Great Grandfather.
I was wondering which side you are researching - Mary or William? If it is the Nightingale side, I would be very interested in chatting with you about your findings. I am most interested in discovering where William's father, William, was born in England.
Regards, Brenda (Nightingale) Despres firstname.lastname@example.org