The problem with PD on Corki is that it doesn't benefit any of his actual abilities, except his auto-attack. I really can't recommend it on Corki with how well gatling gun scales with AD, and now that his missiles do as well.
I don't like Manamune on Corki because it puts off actually dealing damage for far too long. The same goes for rushing a Catalyst. I just hate how long it takes before I can actually rely on my attacks to do something useful besides last-hitting.
For now, I think I'm settled on a 21/0/9 build, with Ghost/Flash, starting with Dual Doran's Blades, and Berserker's Greaves. From there, you can go Sheen, or just grab a BF Sword if you've been farming well. I run mana regeneration seals, and I simply don't have mana problems on Corki like many complain. I last-hit with auto-attacks, harass + last-hit with Q and auto-attacks, and your ultimate uses so little mana it's a non-issue.
So the core winds up being dual Doran's (unless farmed exceptionally well to grab an early BF Sword), Berserker's Greaves, Sheen, and a BF Sword. From there, Bloodthirster, IE, Black Cleaver, Banshee's Veil, and Randuin's Omen are all viable items.
Some other tips include skilling order, R>Q>E>W. Q is always maxed first for burst and blind.
Also, never use E to farm, it costs too much mana and is your main killing tool. Q+R will wipe caster minions and Wraiths in one volley. You can wrack up CS incredibly fast. Last-hit. Get really good at it. And thanks to his passive, last-hitting is that much easier.