If you have already asked the website to remove the content and they will not do it without a court order, you must file an ex-parte motion seeking a subpoena, compelling the ISP to remove the objectionable content and disclose the identity of the "complainer." Ex-parte simply means that the court will consider your motion without hearing from the other party.
A court order is necessary because federal law prohibits an ISP from disclosing the identity of a subscriber unless it does so pursuant to a court order and the subscriber is notified.
ISPs can generally determine the identity of an online poster by tracing the internet protocol address - which is a unique electronic number identifying the computer that is connected to the internet. With an IP address, and the date and time of the posting, an ISP can identify almost any of its subscribers. With a court order to reveal the identity of the subscriber, the ISP must comply.
In order to get a court order, however, you often must file suit first. When a court is satisfied by your pleadings or the evidence supplied that you have a legitimate good faith basis for a suit and that the other party's identity is required in order to advance the claim, then the court will issue the subpoena. Because defamation is (generally) a state claim brought in a state court, court procedures for obtaining a subpoena will vary a bit from state to state, and even from court to court within the state.
Not all derogatory speech is defamatory, however, and not all lies that are posted on the internet are actionable. True statements and pure opinion that does not imply false fact are legitimate defenses to a defamation action. You should have an attorney review the complaints made to see if, first, you have any action and, second, if you
do have an action, to see if the action is worth pursuing. Defamation lawsuits are expensive, especially when they involve anonymous posters on the internet, and you should have demonstrable reputational injury and a solid case before proceeding.
If you received an email from this poster, by the way, it is sometimes possible to determine his identity by the header. This can take some expertise if the sender tried to disguise the origin of the email and his identity, and it is often time-consuming, but it
is often possible.
One other avenue you might want to explore is sending an attorney's cease and desist letter to the poster, demanding that the defamatory content be removed or legal action may be pursued. If you have no email or other address for him, you can have the attorney send the cease and desist to the webhost for forwarding to the poster. Or sometimes the cease and desist can be posted on the site where the original defamatory material appeared - notifying the poster that if he does not remove the material, he may be sued.
However, I recommend you consult with an attorney prior to taking any of the steps above. If you have only one complaint among many positive postings, it could have little impact on you or your business. In fact, many times the person doing the complaining comes out looking a lot worse than the person he is complaining about.
Good luck.