I would not advise getting a degree from a non accredited institution.
An ordained minister normally has the authority to perform a marriage.
Usually the state laws provide any recognized member of the clergy (such as a Priest, Minister, Rabbi, Imam, Cantor, Ethical Culture Leader, etc.), or a judge, a court clerk, and justices of the peace have authority to perform a marriage.
However in some states even the clergy must be first certified or licensed
you should go to
www.google.com and use search words marriage authority and the name of your state.