Alot of people moan and groan when someone picks corki, some even just leave right there. This will end that and have corki come back into the spotlight.
Good tanks will extend past their team to bait and they will take some harassment and turn back. But because they are tanks that harassment is useless. Corki's ult helps some cause it has massive range and does aoe damage so when the enemies are waiting on the tank bait you blast them with a missle and they back farther off. Now the tank is competely alone. Have your whole team focus him down like there is no tommorow. you come in with your W spell casting your E spell and the same time. Then blast him with your Q. All the time blasting rockets and the enemy team if they come to help the tank. If they don't blast the tank then. Unless your whole team is underleveled this wil kill the tank and leave the carries wide open. Then its easy pushing.

Don't forget to use the active of Wriggle's lantern. If you are mid it helps protect you from ganks if your team forgets to call mias. If your team isn't buying wards place it at dragon early game and at baron mid/late game. Also you can teleport to this ward for easy ganks or pushing.
The only thing I would possibly change about this item build is a switch from starks to a Wit's end. And that is only if the tank uses mana. Also if they game comes to extreme late game sell Wriggle's lantern and get a Bloodthirster.
With this items any tank will be dominated from all the on hit effects as well as the reduced armor from these items and your E spell.

This summoner spells work very well with Corki. I suggest teleport for any character doing mid. Which you I suggest you do cuase early farming is easy for corki and it makes up for missing early kills. Also these summoner spells work well late game for pushing after an ace, catching an enemy or running if you got focused in a team fight. Also you can tele to your ward from Wriggle's lantern for a gank at dragon or baron.