What he is doing can be considered harassment. That can be the basis for a FRO. He could not get a FRO without proof and without a hearing that you either attended or were notified to attend. DYFS is a tough outfit.
Important disclaimer: I am licensed to practice law in Oregon, not New Jersey and so can't give advice on New Jersey law. That means that this must be just a general discussion of principles. If you have specific questions, you should consult with an attorney in private.
The law doesn't really have any way of stopping someone from saying things. The best it can do is to hold that person accountable for the direct consequences of their actions, including statements. For example, if someone makes untrue statements about you that cause you a specific harm, you can sue them for defamation. But you have to be able to show a real, cognizable - that is, reducible to a dollar figure - harm that you suffered, as a direct result of the statement. Here, because the children's services people haven't taken any action against you, it seems that you haven't suffered any harm (mere emotional harm an annoyance does not count), so you couldn't sue for that.
Furthermore, calls to child services agencies are generally confidential. So you'd have a hard time proving that your ex-husband made the calls, no matter how sure you may be of it personally.
As you say, in general, restraining orders are only available against people who pose a threat to your physical safety. You can't file for such an order against someone just because they're annoying you.
Furthermore, there is a mad paradox that makes restraining orders, in my opinion, almost useless most of the time: You obtain a restraining order when you believe that someone intends to do you serious harm. The order makes it illegal for that person to come into contact with you, so that they will not be able to harm you. But it is already illegal for the person to do you harm at all. If they really mean to do so, then the threat of legal sanctions clearly does not deter them, because they are already set on violating the law. All a restraining order can do is to allow a truly violent person to be arrested a few minutes earlier into the commission of a crime - or send a message of social disapproval. In my experience, this is what most people who file for restraining orders really want: For a judge to shake their finger at the other person and say "You've been very bad!" But this almost never happens - and is not a legitimate use of the court's time.
Ultimately, my best guess is that you can't do anything within the legal system about this. The law doesn't have a solution for every problem in life or for every wrong that someone can do to you; it can't be an arbiter of all personal conflicts, and it can't make crazy people less crazy. The only thing that really helps with such people is appearing not to care about what they're doing - this usually makes them get bored and stop, or find something else to fixate on.
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Although it is not difficult to get a TRO, the FRO requires more. Be sure to defend this, preferably with an attorney. I agree the false complaints against you are harassment.
Please be advised my answers to questions does not constitute legal advise and you should not rely on it, due to the fact that we have never met, I have not been aprised of the facts in you case nor have I reviewed any documents.