It really depends on the individual program as to what they will allow. If it is allowed, it would depend heavily on what the felony was for. Anything that would be considered a violent crime or a danger to the children would almost definitely not be allowed.
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Most(all?) organizations that have adults inter-acting with kids conduct background checks on their volujnteers and employees these days. When the league does a background check on you they will probably learn of your conviction and, in todays climate, I'm sorry to say that it is doubtful you'd be allowed to coach.
I don't know the answer, but maybe you should just stay away from the kids, dude.
I doubt it. When working with children a background check is done and that would show up.