If you can't choose a target opponent when you put Manticore of the Gauntlet's triggered ability on the stack (most likely because your opponents have hexproof), the ability is removed from the stack and you won't put a -1/-1 counter on any creature.

If either target becomes illegal after Manticore of the Gauntlet's triggered ability is put onto the stack but before it resolves, the other is still affected as appropriate.