I've been gaining ELO... er, League Points... pretty steadily, mostly playing adc, but I run into trouble when I have to face a Nunu + Caitlyn lane.

Are there any good adc/support combinations against them other than Graves + Leona? (I haven't practiced Graves much).

I main Ezreal, and Cait causes some problems for me.

soraka support with you beats that easy. I love playing raka add me to friends if u want to try it in game.

Nunu and Caitlyn have no form of sustain so an equally aggressive lane like Ezreal+Blitz or Ezreal+Taric can work out pretty well given that you have better CC.

I especially recommend Ez + Taric due to the free bonus armor (taking away much of the damage) and the sustain.

Another decent combo is, as aforementioned, Soraka since she has a high range silence + nuke as well as good heals.

Aggressive early game champions like Miss Fortune, Corki, or Graves is pretty good.

Otherwise, Nunu Vayne can just stall the lane and pwn later on.

As it's been mentioned, that setup lacks any early sustain so you'll want to press that advantage.

Thanks for the tips! I'll try to get my support to play Taric or Soraka the next time I see Cait + Nunu

A well played Sivir will counter them hard. Especially when lanes with a sustain support like soraka or sona with mana manipulator. You can eat her poke or nunus with your shield. If she lays traps, pop your shield and walk over them. Free mana. Her boomerang blade helps you poke and farm minions from range. Her ricochet ensures last hits when minions get pushed under tower.

Truely though, most any ADC will outperform Cait in the end game. Her kit is good early, but unless she gets a huge lead in farm/gold, falls off late. Survive her peak around 9, and flatten her late around 18.