Okay, this thread has been weighing heavily on my mind and I finally figured out why.
It bothers me to think of punishing a puppy who is already stressed and is telling you about his distress the only way he knows how.
In addition to NEVER reinforcing behavior that you don't want (whining, barking), this is what I'd do. I would try to prevent it from happening.
I'd try to make being left behind a GOOD thing. I'd start giving him/her their meals just before you left the room. I'd give them Kongs and then leave the room. I'd give a new toy - or rotate in an old one that they haven't seen in awhile - just before leaving the room. Give a small treat when you leave.
In each case, I'd try to return to the room before the pup starting stress-vocalizing again. You want that time when they're alone to be a pleasant time; you don't want to leave them long enough that they get uncomfortable again.
You should be able to gradually lengthen the time that you are out of the room without the pup fussing.
Give it a try and then let me know how it goes, okay?
Oh, I've also had pretty good luck with teaching Joey a "quiet" command by reinforcing small, but increasing, increments of quiet behavior with praise and small treats.