Sivir is one of the best counters to Caitlyn. Due to the long cast time of Caitlyn's abilities, Sivir can easily block the damage and regenerate mana with her Spell Shield.
Jinx, despite attacking at a shorter range than Caitlyn, can out-sustain and push down the lane's initial tower faster. Varus's Piercing Arrow is a great way to zone out Caitlyn, inflict damage and keep out of harm's way. With Lucian's gap closing and burst potential, he makes a good match against Caitlyn. Despite the champion, when fighting Caitlyn, stand behind minions to decrease of the damage of Piltover Peacemaker, initiate when her net is on cool down, and never fight her while she's in a bush, as it increases her passive critical chance.