what is needed for a defendant to waive a jury in civil case in dockland country new york usa?

Assuming the case is in in the Supreme Court of Rockland County, and not some other court which may have different rules, a party, usually the plaintiff, files, through his or her attorney (unless htey are acting pro se) a document known as a "Note of Issue" when the case is ready to be placed on the trial calendar.  At that time, the party filing the Note of Issue notes whether he/she/it wants a jury trial or not.  If the party does not indicate that a jury is desired, the other party (generally the defendant) can then request one.  IF they don't, they waive their right to a jury trial,  Thus, assuming that it is the type of case where there can be a jury (some equitable claims must be decided by judges, not juries), the case will be tried before a jury if either side (by their attorneys) timely requests one.