Dorans Blade > Berserkers Greaves > Infinity Edge > Dagger > Vampiric Scepter > Black Cleaver > Phantom Dancer > The Bloodthirster > Phantom Dancer > Phantom Dancer. You sell your Dorans Blade when you need the 218 coins, and you sell you boots to make rooms for your 3rd PD, you Dagger is a component of you Black Cleaver, and the Vampiric Scepter is a component of The Bloodthirster.

I think it would probably be trin-force-ish. Corki has good harass, and that's not just his skills. His passive makes for really nice damage. Considering the build I would probably use for corki, would be along the lines of Trinity Force, maybe a Phantom Dancer or something else with ASPD, and get some Attack Damage through Bloodthirster or Infinity edge. If you want to go a little more durable/tanky, grab a warmogs on your way to atma's(but only if you get health items, such as frozen mallet or something). Another good suggestion would be Madred's bloodrazor, for the magic damage. Combined with corki's passive, it would make it easier for him to take down tanks. If the enemies are all quite tanky, try getting some Armour Pen.

Note: Try changing the build: For example, if the enemies are squishy, there would be no need to stack Armour Pen. Instead, go for some health-attack damage, as the squishy characters seem to do more damage than the moderately durable ones.

Don't forget, if you want to be tankier, and there is a karthus in the game, the best way to annoy him is to buy Maw of Morthius.

Good luck with your build!

The Big 100k

The pure supports are those that will benefit their ADC lane partner in the bottom lane directly by healing, improving resistances, or the like, yet they tend to be squishy. Examples of these would be Sona, Soraka, Zilean, Lulu, Nami, and Karma. Some supports provide a great amount of crowd control (CC) or other abilities that make it easier for the ADC to secure the kill and are generally tankier than the pure supports, such as Blitzcrank, Leona, Maokai, Thresh, and Nautilus. Then there are those that are a bit of a combination tank/support and are generally built as such, including Alistar, Taric, and Galio.

I think Taric is one of the best, as he can heal, has an ability that provides an Armor bonus to all surrounding allies, has a very reliable stun, and an ultimate that increases AP/AD for all neaby allied champs. He packs a good deal of burst damage and is tanky to boot - excellent all around support/tank. If your ADC lane partner is mana hungry and needs to spam abilities for maximum effect, like Ezreal, then Soraka is a good choice because she has a no mana cost ability with the utility of either giving mana to an ally or silencing/damaging an enemy. She can also heal with a regular ability and her ultimate in addition to increasing MR with her passive. Sona is great since she can deal a great amount of poke damage and constantly has auras active as part of her abilities, with the ability to heal as well.

Each support can be nearly equally useful to their lane champ, however, if played well. Choosing your support is situational as well, since if you already have a tank that is going top or jungling, it would probably be more useful to the team to have a pure support instead.

League Of Legends Champions Guide : elohell.net