How would I get married out of state on a Sunday?

Live in MI and looking to get married on a Sunday in Illinois. I know I need to apply for a marriage license and get an officiant to certify the license but I'm a little confused as to how it works in between states as well as getting it completely done on that Sunday. Do I apply up here or wait til I head down Saturday? Are courthouses even open on Saturday? Really looking to be married on the specific Sunday. I don't wanna be certified Sunday and then not be officially married til Monday.