(This moveset is for Gen. 5, White 2/Black 2, to be more specific) Also, it's more defensive, so it should most likely be used to stall.
Probopass @ Leftovers (if you chose Snore) or Chesto Berry (If you chose Power Gem)
Nature: Lots to choose from:
(Offensive): Modest (+Sp. Attack, -Attack), Quiet (+Sp. Attack, -Speed)
(Defensive): Bold (+Defense -Attack), Relaxed (+Defense -Speed), Calm (+Sp. Defense, -Attack), Sassy (+Sp. Defense, -Speed)
(1) 252 Sp. Attack, 252 HP, 6 Defense
(2) 252 Sp. Attack, 252 Defense, 6 HP
(3) 252 Sp. Attack, 252 HP, 6 Sp. Defense
(4) 252 Sp. Attack, 252 Sp. Defense, 6 HP
(1) 252 Defense, 252 Sp. Defense, 6 HP
(2) 252 HP, 252 Defense, 6 Sp. Defense
(3) 252 HP, 252 Sp. Defense, 6 Defense
Iron Defense or Lock-On:
Iron defense is really good for a defensive Probopass, because it increases the users stats by 2 stages(?) It can be learned at level 1, or you can teach it move tutor. Combined with the Leftovers, it will really stall for awhile. Lock-On works good for an Offensive Probopass because other moves are sure to hit. This move is learned at level 50 (same for Nosepass).
Zap Cannon: Is the best move that Probopass can learn. It's learned at level 50, but has low accuracy. Of combined with Lock-On, it is sure to do some serious damage. And it also covers it's weakness, Water.
Rest: This move is really good for annoying your Opponent, because if it has high Defense/Sp. Defense and HP, it will take awhile for the opponent to lower it's HP, and it works well with it's ability, Sturdy. Even if it's hit with a Fighting, Water or Ground type move, it will survive, and you can just restore it's HP. This move is learned at level 22
Snore, or Power Jem: Snore will only work when Probopass is asleep, and when it uses rest, it will be put to sleep. So why wait a few turns to attack, when you can attack the next turn. Or, you can chose Power Jem, for STAB. It has higher accuracy, and will more damage than Zap Cannon.