Is the louisville court house open on sat and can we get married on sat.

The courthouse is not open on Saturdays,

Any of the judges and justice of the peace can marry you. Also the clerk of the court should have a list of ministers in the area that will also marry you. ( often the ministers may marry you cheaper than the judge does)

The clerk of the court can make an appointment for a marriage with one of the judges

Jefferson County Clerks Office (http://www.jeffersoncountyclerk.org/side-bar/faq/marriage-licenses.asp)