Yes, you use more muscles standing than sitting. By having black coffee you'd be taking in even less calories , mind you if you're having bikkies with it I'd just sit down!!
For Gods sake sit whenever you can, sod the callories think of your well being when you're older. Relax when you can think of your poor old bones they need the rest. Don't abuse them or they will let you know all about it later on. (from one who knows)
If you sit on one of those exercise balls you will use a lot more calories because you use the muscles to balance and you don't actually drink the coffee because you spill it all.