Highly unkillable champions are a problem for AD champions as well, it just comes down to when you start bursting them down.
If you're going one vs. one against tanks you can always build for a longer but more sustained burst. Building items like Deathfire Grasp and Lich Bane will essentially give you 2 more bursts in your rotation, and Rylies will allow you to kite. Frozen Heart is pretty nice to, if you're going up against a super-sponge target you'll need to survive long enough to get multiple rotations off.
Like ADCs, you'll generally need a substantial reserve of cash to pull this off well though, in modes like Dominion or Twisted Treeline tanky DPS will generally run you into the ground with their early advantages of being both tanky and DPSy before you can get much gold.
Of course, it depends on who you play. With Malzahar you just stack AP and throw a Void Staff in the mix.
When all else fails, a decent number of Mages can work as an ADC as well, all that really matters in that regard is having a ranged attack. And a decent chunk of mages actually have something that scales with AD. If not, you can end up being like an Ashe with lackluster ADC damage but loads of utility.