they hurt my children one went to a hospital i cut off service still owed them money do intent to pay they for all they did watch my children
Craigslist is for sale of things, so I'm not sure how anyone could slander anyone on it. Anyway, Craigslist posting expire on their own, and if there's an offending post, complain to the site itself.
As for the merits of a claim, defamation (slander is oral, libel is written) requires provably FALSE FACTS, not opinions, and not just something that's unflattering, which is communciated to others that harms you. If you did owe someone money and they advertised that fact, that's a fact, and it's not defamation, even if it embarrasses you.
If there's more to your story, see a defamation lawyer for help.
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Securities / Investment Fraud Attorney
The first thing you want is for these people to stop besmirching your good name, and this would likely be done through filing for injunctive relief in Davidson County Chancery Court. But the first thing to do is to demand that these people stop and take the postings down immediately without the use of the courts.
While "slander per se" is a tort, proving up your damages may well be difficult. But at least TN does have a Chancery Court, which generally has an ear for equitable relief in matters such as these.
The foregoing is not legal advice nor is it in any manner whatsoever meant to create or impute an attorney/client relationship.