This is either
Jane Ray 1794 - 1820 wife of Rev Samuel Barker
or
Mary Ray 1792 - 1872 wife of Samuel's brother John Barker
NB Jane died aged 26, is this a portrait of someone under that age
and
If there were two Mrs Barker's late Miss Ray of Tannington at the time of the sitting
I would have thought that the sitter would be fully identified.
Ron Goose's view is that it is Mary.