My usual arsenal against whining consists of jokes, sarcasm, and acknowledgement. Usually any one of those, or a combination of them (along with persistence) quells the whine.
Yesterday, one of my really cute - usually well behaved - kids whined her head off. It might have been the rain. It might have been the soda her mother allowed her to bring, and sip, in art class. Whatever it was, it took all my will power not to slap the kid upside in the head to make her stop.
It really brought down the rest of the class too. It only takes one bad orange to ruin the box right? Well, that last half hour of art class was one of the longest I've ever taught. I went home exhausted from keeping up the energy level and keeping down the discord.
Kid, if you have enough energy to whine more than the cellar of a high-end French restaurant, then you have enough energy to pick up that pencil and draw. Redirecting that energy is the tricky part.