defamation of character

What is the name of your state? florida
wife was school aide in religious school and was terminated becasue a parent accused her of throwing furniture in classroom even though the Teacher in the room never saw it happen. was wondering if there was legal recourse against school and/or parent

It's not necessary for there to be an eyewitness. Barring a contract or CBA that says otherwise, an employer is allowed to terminate on suspicion of wrongdoing. You aren't saying that she didn't do it; only that the teacher in the room didn't see it. But even if she didn't, the employer is permitted to terminate under these conditions. I see no case whatsoever against the school.

If she is prepared to prove that the parent deliberately and maliciously lied for the express purpose of causing harm, and there is no chance whatsoever that the parent was honestly mistaken, it's possible she might have a case against the parent. Speak to a local attorney about laws in your state.