Where does the saying a rum deal come from?

The actual phrase is a "bum deal," probably because "bum" means of little value, so a person who gets a bum deal loses something or ends up with less than the person on the other side of the deal.

When the phrase "a rum deal" is used, someone is usually just playing with Words, meaning "a bum deal" that involves liquor, and sometimes, the Caribbean (since this is the source of most rum).