Joseph Congdon was born 18 April 1765 in Exeter, Rhode Island - Rhode Island, Vital Extracts, 1636-1899 (this is an Ancestry record and will require a subscription.)
His parents were John Congdon and Mary Reynolds (hence Benjamin Reynolds Congdon's middle name).
Hannah, his wife, was Hannah Brown/Braun. She was born 19 November 1780, in South Kingstown, Washington, Rhode Island. Rhode Island, Vital Extracts, 1636-1899 (this is an Ancestry record and will require a subscription.)
She was the daughter of Jeremiah Benjamin Brown and Eleanor Lillibridge.
There is a possibility Joseph was the son of George Congdon and Ann Daughs. Same family. George was the brother of John. On the 1820 census, they are all pretty much living by each other. The record even tries to sort them out by saying 'James of G Congdon' and does this with a couple of similar names. Here is the FamilySearch information, but there is not a birth record that I can find for him yet, so hold this with a grain of salt for now.