This is usually a tough case, and expensive to pursue. If the items are clearly defamatory, however, then either (1) any injunctive order you might get or (2) any fear of a large money judgment you might instill in the persons propagating the lies might get you the relief you seek.

A strong demand letter from an attorney might also shake them up and get some action.

There is also a measure of gamesmanship that claimants sometimes use in such matters. For example, a well-known "patent troll" sued an in-house lawyer from Cisco in a recent much-publicized libel case for blog postings to the effect that the troll had conspired with court clerks to alter the filing date of a complaint where such filing date was critical to the outcome of a case. Owing to liberal jurisdictional rules, the parties involved (including Cisco) were forced to defend the case in a remote forum (in Texas) where sympathies were strong in favor of the claimant.

All this turns on the specific facts. If the statements have a color of truth about them and constitute a customer's exercise of free speech rights, you may have an uphill fight in getting formal legal relief.

Of course, there may well be steps you can take here besides the purely legal but I assume you will consider these as well.