It's countable. Generally, a person has an excuse, but may over time have several. When he finally gets round to doing it, he has 'run out of excuses'.
So 'You should have no excuse for not coming to the game' is right. But the plural is possible - a teacher might say: 'You're all coming to the game, and I want to hear no excuses' (presumably the teacher isn't expecting to hear more than one excuse from each pupil, but might).