A friend of mine pulls off a great Caitlyn Counter with Tristana, because of Tristana's passive, which increases her range as she levels up. Eventually, her range supersedes Caitlyn's naturally at level 16, and matches it at 15, but Tristana has superior objective takedown skills, multiple escapes, and overall better firepower. Furthermore, to further even the playing field, Rapid Firecannon has a passive that increases range every few shots, while also granting stats favorable to Tristana.
You can attempt to outpoke her with champions that have low cost long range abilities, like Jhin's W (2500 range, 50-90 mana, but Jhin rarely has mana issues due to the combo of his passive and Essence Reaver), or Jinx Q (range 750, 20 mana per attack), or even Graves' Q and W (950 range each, one of which deals massive physical damage, and the other giving her her near sightedness so she can't attack you nor see your movement, all the while dealing magic damage).
Additionally, CC heavy supports like Blitzcrank and (my personal favorite) support Nautilus make it so that Caitlyn can't escape the range of hard hitting short range ADCs like Graves, Jhin, and Lucian.
Teemo can stop her auto attacks with his blind, and make it unsafe for her to be in lane with his traps. He has an escape in his W, and passive magic damage on his E to discourage damage trades.
The beautiful thing about League is that there is always multiple ways to skin a cat or counter a champ.
Except Teemo. There's nothing you can do about him.