The Court of Yun-Coria was anywhere where the members of the Court were present and judging. One such example was the damutek on Korriban. It was based upon the teachings of the Yuuzhan Vong goddess Yun-Coria and her servant/"messenger Yun-Avengane. The Court was comprised only of members of Domain Coris.
At the time of the Yuuzhan Vong War, the leader of the Court was Eg'roeg Coris. The Court had experienced a loss of many of its members, because of the New Republic's attack on the dying worldship at Sernpidal.
Most members of the Court lived on the worldship, Coria's Judgment.
The most noticeable trial the Court ever presided over was the "trial" of Jedi Master Nathaniel Kenobi Solo. Through contacts he had paid in the Peace Brigade, Nathan had learned that the Court could not make a decision, until the accused quit talking. So, being his normal, jocular self, Nathan went into a monologue, of which was said to have lasted over an hour before the intervention of Darth Mutatos and the combined forces of the Jedi, the Original Sith, the Korribanites, and the Massassi.
After a short, but bloody battle, all of the senior members of the court were either dead or dying. This led way to elections, of which, were carefully monitored by Supreme Overlord Shimrra Jamaane. Who wanted the Court to reflect his word only.
After the debacle on Korriban, Nathan was widely considered by the Yuuzhan Vong, to be Yun-Avengane's mind and spirit in human form.