Do the coach cards allow players who already have the specified skill to use it twice?

For example, would a tackle coach allow a Blitzer to tackle twice when he is deployed?

yes.

as they are matchup action and played after using all the skills already.

So the skills of the committed player don't matter anymore

Thanks for the help Luckyfer. For some reason I've been playing the coaches wrong all this time. This makes the tackling and passing coaches that much better!

Also there is no limit on skills per se - each icon is a tackle skill, or a sprint skill and so on, and there are plenty of players with more than one icon of the same kind (Skaven Gutter Runners with two passing icons, several with 2 cheats etc etc). So there is no actual implicit bar to getting the skill again anyway so far as I can see - useful point if someone doesn't like the 'its after' logic of the matchup action.