Corki is a special champion as he is the only ad carry that has AP and AD and is a real hybrid carry. so because of that you can really take any item with Corki and it would work. want some AP? pick void staff. want some ad? pick Infinity edge! The only flaw with Corki is that he has no Crowd Control. But THERE'S A FIX FOR THAT!
Rylai's Crystal Scepter
the idea is that it work a bit like a Brand support and that every ability will work well with Corki.
Q Phosphorus Bomb is just a big nuke of damage(now with extra slow!).
W Valkyrie not only is a escape but now the trail will slow the enemy making it even better.
E Gatling Gun is a constant slow to an enemy target and
R Missile Barrageis basicaly constant poke but with and extra slow.
The fact that every thing works so well with rylai's make corki really good as a Poke support.

Glacial Augment Is kind of a way to have a early slow, but you can still go thunderlords(electrocute) if you value the DMG

Corki Support will play more like a second Mid lanner than an actual Support. so i would really recomend to take From the Damage tab Hextech Gunblade Morellonomicon Void Staff

the defense tab is only if...

1. you have no tank in the team
2. your adc is so fed that he could really you the Zeke's Harbinger
3.you're really behind and need the tanky stats

but even then i would still recommend to take the damage as corki is just an all around safe champ

because of your passive, magic Pen is just really good as your Auto attack will do more damage. Thats also the reason you build Void Staff instead of Rabadon's Deathcap

Pros
1.every ability can work well with Rylai's Crystal Scepter
2.you can poke for days
3.you are basically a second mid laner

Cons
1.you are a squishy target for any assassin
2. you dont have any heals for you ad carry
3. if a champion has more speed than you can slow them you are ****ed!