Assuming the felon is no longer incarcerated, it’s probably possible in theory, but your state might have some statute prohibiting this, and you should check with an estate planning attorney.
On the other hand, why appoint a trustee whose past conduct, especially if the felony involved some sort of fraud or dishonesty, would cast doubt upon their conduct in any court proceeding? Even if the trustee did not behave inappropriately, the appearance of impropriety might lead to litigation. I’d suggest staying away from this situation if possible.