As it's been a while since your previous post, I'm thinking you might have already found the birth record for Permelia Pettingill.
However, if not, I found a birth record for her in Hampshire County, Massachusetts. She was born the 13th of June 1788, in Worthington Twp., to Samuel and Hannah Pettingill.
Samuel & Hannah moved to Fort Ann, Washington County, New York circa 1792. This was taken from Samuel's Revolutionary War pension application documents.