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The buyer is suggesting that for you to claim that they are not paying their bill is defamatory, i.e. a false statement of fact, concerning the buyer, made to a third party causing damages. This could be true, because apparently the buyer "is" paying, although perhaps not timely.
You may want to consider not expressing anything negative about the buyer to the school district. Your issue is between you and the buyer -- the school district is not involved.
So all I can do is small claims?
Yep. If the checking account were empty and you were paid nothing, you could call the police, because that would make a case for theft by deception (intentionally bad check). But, in this case, the buyer is paying something, so it's not obviously a crime.