Have you tried other spellings?
I am researching DURE. I know there were DUREs in Scotland. I have often run into misspellings of DURE as DEWAR, DUER, DARE, etc. , although DEWAR is the most common. Also DUREE, which is actually the original. So you might try these. Some Scottish ones came to Canada, but they are not mine.
Unless you know otherwise, it's possibl that yours were originally DURE, which goes back to France originally, with double e; accent acute on the first e. When I say "originally", I am not yet sure how far back. There is reason to think it could be as far back as 1200s, acc to records in Devon. I haven't figured out that part yet.