If something is unpromising, it doesn't show signs that it's going to be successful, beneficial, or fun. An unpromising school dance has bad music and boring snacks.
An unpromising TV series seems dull from the first episode, and an unpromising job interview is awkward and uncomfortable. Just because something's unpromising doesn't mean it won't work out well in the end, only that it seems unlikely. After an unpromising start as the sickly runt of the litter, your dog may end up growing into a 100-pound goofball who lives a long, happy life.