Real talk, Zilean support sucks in laning phase and only does really well in certain team comps. Building AP on Zilean support just makes him into a crappy poke mage that will be blown up in every fight. It's better to go tanky, max your e, and ask to be camped. He scales really well into late-game if you just focus on utility, forcing engages/locking down opponents with his e, getting stuns off with his double bombs, reviving carries with his ult, and soaking up a lot of damage with all the health in a tanky-support build path. I got a video somewhere of me zooming all over the place as an unkillable tank-zil, annoying the shit out of the enemy team. Rammus is your best friend with this setup...
Karma is the ultimate poke support. She's a lot like blue Ezreal in that 90% of her damage is spamming q. She's extremely dominant in laning phase if you play her well, and you'll need to because she falls off in terms of utility later. If you want to play Zilean as an AP poke support, just play Karma instead.