File in a foreign court a libel lawsuit against a U.S based publication? That's an ill informed decision.
The United States (on the federal and also on some States’ level) passed laws barring enforcement of foreign libel judgments issued in countries whose laws are inconsistent with the freedom of speech and Due Process granted by the United States Constitution.
New York State legislature unanimously passed the Libel Terrorism Protection Act The law offers New Yorkers greater protection against libel judgments in countries whose laws are inconsistent with the freedom of speech granted by the United States Constitution.
As of July 2010, six other states have passed analogs to NY's Law: Illinois, Florida, California, Tennessee, Maryland, and Utah.
A federal law called the Speech Act was based on New York's law. The burden of proof is on the party suing for enforcement of the foreign judgment in the U.S. The party seeking to prevent enforcement of the foreign judgment in the U.S, may also sue the libel plaintiff for a declaration that the foreign libel judgment is "repugnant" to American constitutional law, and therefore, may be entitled to attorney's fees for resultant legal proceedings.
In sum, if Cyprus libel laws do not protect free speech and Due Process like the U.S Constitution does, then the Cyprus judgment is unlikely to be enforced in the U.S, and plaintiffs risk an award of costs against them by a U.S court. For further details see my comparative law text book
http://foreignjudgmentsinisrael.com/