Q: Can a business put on the fine print of their contract that clients can never post negative reviews online?

A: You can put just about anything you want in a contract that is not illegal activity, though there are some clauses that a court may deem to be unenforceable in court for various reasons. The clause you mention is probably enforceable, at least for a reasonable period of time. (A court might not enforce the word "never".) When you sign any contract, you are responsible for reading and understanding everything in it, including all fine print. Many parties to contracts make the mistake of not bothering to read everything, leading to legal problems and disputes. Some types of contract, by law, must have certain text of a certain sized (for example, certain loan agreements), but there probably isn't a statute requiring the clause you mention to be larger than fine print. If it is enforceable, then yes, the business can sue a breaching party. How much money the business would be able to seek in damages is a whole other story; that would partially depend on whether the contract includes a "liquidated damages" clause.

A: If you sue, it'd be defamation.

A: While a business may place its policy in fine print, the question is if that policy is enforceable. One must review the entire contract, and make sure that (s)he acknowledges and accepts its content. On a practical level, it would not make sense for a business to contemplate suing a client for a negative review--the reputational damage may far exceed the client's review.