I also agree with Jutschge's answer, with Leona/Thresh/Blitzcrank as a counter support to Zilean, but don't forget the shielders.
I just want to add this info since I usually play as Zilean.
The common Zilean moves are: (from a less active to a very agro type)
1. Wait on a lane and do nothing. (could be DC)
2. Get into range and Q the ADR (+ or - AutoAttack), then run back.
3. Expend more mana, using E to get into a closer range, Q to the ADR, W, then Q to the ADR(+ or - AutoAttack) and then run back.
On which the answer to 2 and 3 are shielder support, since Zilean's Q has a huge delay. (the enemy shielder can even count three seconds before actually shielding the ADR or the support, or whoever needs it)
I get really upset if the enemy support use shield, because everytime I cast the bomb, most of the time, there would be a shield that will somehow soak up the damage, and less damage means I need more mana to expend so that my damage would really get through the shield. And since mana is Zilean's problem then it really is problematic.
So, try teaming up with Janna/Lulu/Lux against a lane with Zilean support if you usually play passively/bait. And Leona/Thresh/Blitzcrank if you play actively.
Sorry I can't comment yet but I just want to share one of Zilean's weakness.