Zilean's Combo and a Small Change
So it's not secret Zilean is weak right now. He's been pushed out of a mid lane entirely and is considered a weak support. Why is that? Because his only damage was nerfed and turned into a skillshot that's not very easy to land. Along with this, part of the problem has to do with people not understanding how his kit works. To alleviate one of the problems, here are the combos you can perform to get the most out of Zilean.
How to combo Zilean's new kit Example A: Use timewarp on yourself, land bomb, use rewind, use time warp on enemy, bomb, then you get the stun. You use the speed up on yourself first to get into range while the enemy isn't expecting it. It's dangerous because it's not easy to land the bomb when the target isn't slowed.
Example B: Use timewarp on the enemy, land an easy bomb, rewind, bomb on the enemy again to land a stun. This is a lot more reliable for landing the stun and a good way to peel for your adc. The negative is, no one will let you walk up to them to timewarp them so it can only be used as a peeling tool. If you do walk up to someone like this you're probably going to be blown up because you're super squishy Zilean. That's always been his weakness.
Suggested Change Right now, his stun is conditional on landing a bomb on a target twice. This is extremely difficult to do. What I suggest is to keep the mechanic the same and add a debuff. When an enemy takes damage from Zilean's bomb it places a debuff for 5-6 seconds. When the second bomb goes off the inner radius will stun all enemies with who have the bomb debuff still on them. This allows some room for error when Zilean doesn't land two bombs on the same target.