Dodge the.... Ok. Sorry, I had to.
In all seriousness, it depends on your Support. Zilean is one of those supports that can win his lane for his ADC solo if both enemy laners don't cooperate.
You have two general options against Zilean:
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Sustain support and just have a boring farm lane. This is especially true once Zilean hits level 6. Even dedicated kill-lanes will have trouble against a Zilean post-6. His bombs do a lot of damage, but not enough to overpower healing/shields from Soraka/Janna/Nami/Sona, etc. Basically you dodge as many of his bombs as you can, but otherwise ignore him and wait for laning phase to end.
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A super-aggressive kill-lane. Zilean's CDs are fairly long early game. He can double-bomb ONCE, but then he'll be stuck with auto-attacks for 8-10 seconds. If you can catch him out of position, go for the kill. If you have a Blitzcrank, Leona, etc? Followup if they engage onto him. However, once he hits 6, you aren't going to win all-ins without ganks or being really far ahead.
The biggest thing with Zilean is that you cannot win short trades with him. You either need to play entirely passive with a sustain support, or you need to commit every time you manage to catch him. Can't do half-and-half against him.
In blind pick, you're SoL... but in Draft, try to match up your choice of ADC with your support. If they took Soraka, Alistar, etc? Pick a late-game carry like Tristana/Jinx.
If they went with an engage support, like Leona or Blitz? Take an early-game ADC like Graves or Miss Fortune.