Some states have laws specifically prohibiting felons from working with children, which would automatically disqualify them from coaching. Other states might have background check requirements that could reveal a felony conviction and lead to disqualification. Even if state law doesn't explicitly forbid it, individual school districts might have their own policies that bar individuals with certain types of felony convictions from coaching.
The *type* of felony is also crucial. A non-violent, non-sex-related felony might have a different outcome than a conviction for a crime involving violence or children.
In short, a convicted felon would need to check their state's laws, the specific policies of the school district where they wish to coach, and possibly seek legal counsel to determine their eligibility.