I've gotten hiccups from Hydrocodone. I cure it by doing what the poster above said, holding my breath. I do it for about 10 sec. then take a few deep breaths, and if that doesn't stop it I just repeat it until it does. It usually works. If not, try drinking a shot of vinegar.
I didn't read beyond the first post, so this may have already been answered, but both opiates and benzos suppress the respiratory system, which means they affect your breathing. This can cause hiccups. Pretty simple logic.