The top picks not in lane to counter Caitlyn include Nidalee, Naafiri, and Sylas. These are all good at countering Caitlyn with high win rates over 57%. Even if these Caitlyn counter picks are not played in your lane, it's not a good idea to take her into any of these matchups. They will likely crush Caitlyn.
Conversely, if the enemy team choses either Amumu or Swain, Caitlyn mains should strongly think about selecting her, as she easily wins against these selections with win rates over 52% against each ofthem.