People forget that while Zileans bombs are really annoying he only has 1 at first level. Which is the best time to gank him. Depending on his lane partner be aggressive on him. And an underleveled underfarmed zilean is your best friend.

Most people have covered it, but:

• Counterattack when he bombs. He only has a flimsy autoattack and one skill that does damage. Once the bomb is on your head is when the window is open to attack him. If you DON'T counterattack, you are just giving him free damage and will eventually lose that battle.
• Wreck him at level 1-2. His bombs do little, and at level 1 he doesn't almost nothing.
• Some champions are counter bombs decently, mostly champions with shields such as Janna, Morgana, Malphite, Urgot, etc. Since you get some warning before the bomb goes off (at least the second one!) it's easy to shield yourself or lane partner. If you have these champs in your game, switch lanes for the good matchup. Sometimes you'll want to switch even subpar matchups around if you can at least get someone who can harass back more effectively.
• When bombs are on you, make sure you stand near your own minions. Blow up your own creeps to pull towards your own tower. (Ideally don't give Zil more minion kills, but better than that fighting Zil at his own tower.

Remember that Zilean can just ult himself when you manage to counter him and kill him, letting him live another day

Silence.

I have a friend who likes to lane zilean, and he rages everytime someone with consistent silence goes against him. Remember post 6 if he gets low, silence him and then go for the kill so he cant pop his ult.

its impossiblu!