I have tried Find My Past and Family search. Unfortunately with no luck.
I have a birth certificate of their daughter Clara Fortune Gifford (1838 in littleham exmouth) mentioning them both. I can also see Ann and Clara on the censuses.
Nathaniel also died in Littleham 1838, so I tried looking for a marriage there, but no luck again.
I know Nathaniel's first wife Fortune died in 1830, so they must have been married sometime in between then and when Clara was born.