There's a lot of options for an Irelia player with runes. Conqueror, Triumph and Last Stand are necessities. Conqueror synergizes with her kit perfectly and she is balanced around it. Triumph is amazing because it makes you survive dives that would be a 1 for 1 trade otherwise. Coup de Grace is always going to do less damage than Last Stand on a drain tank.

For the Legends, the choice between Bloodline and Alacrity is based on your playstyle. Take Tenacity when they have a lot of crowd control.

For your secondary tree there's 3 viable options. Resolve, Inspiration and Domination. Pick depending on your playstyle.

Personally I run Resolve almost every game for Demolish. If you have Demolish and you kill your lane opponent or force them to recall, you get about half a kill from plating gold. It also greatly helps in the split. Second Wind is good versus heavy poke. Bone Plating is good versus matchups that want to get up in your face and beat you down. Overgrowth and Revitalize are options too if you just want to scale but they aren't useful in lane.

From Inspiration, you can take a combination of Biscuits, Boots and Timewarp Tonic. Inspiration is good for early game but once laning phase ends it's severely lacklustre, so personally I dislike it.

From Domination you'll want Taste of Blood/Sudden Impact and one of the X Hunter runes based on personal preference.