So often we (and I mean me, too) back children into a corner by asking "did you do this?" when we know very well what they did. I've learned to say things like, "I heard you yell 'you suck,' on the field today. That kind of language is not acceptable. You have the choice of apologizing to ________ or missing the next two games. What's your choice?" Then stick to it.
Sometimes we have to go on circumstantial evidence. I generally believe the child unless the evidence or my own ears and eyes tell me differently.