Trundle, malphite, olaf all outlane her and beat her ass at what they want to do. For malphite it is teamfights for the others it is skermishes and splitting. There is no true counters against her so don't expect to do everything better but those two can beat her.
If you are going for matchups that require you to actually do something there is Nunu (slightly troll though, but there is nothing irelia can do in lane), fizz, darius, maokai, nasus, tryndamere, and udyr. Those are not as solid but they are favorable in lane and then either become better midgame at what they do, or outscale her for lategame.