I don't think there is a way to attack, unless someone has a program/custom script for mapping buttons to specific actions.
I mean, with Damon's style, I have done the football tackle attack twice, but it seemed to be done randomly, and only when others NPC's are helping me out. I could be wrong, though. Maybe there's two buttons you have to press at the same time, like how with the mid-sized greaser's roundhouse kicks you have to press alt and shift at the same time.