Can I get married at the City Hall on a Sunday?

Chances are no because most City Halls are closed on Sunday.

Where you can get your marriage license in Cook County

Vital Records (http://www.cookcountyclerk.com/aboutus/hours_locations/Pages/VitalRecords.aspx)

And no, Marriage at government offices are done only at specific times M-F, and the culturial center on Saturdays.

Judges can be hired ( as a pastor can) to do onsite weddings or weddings outside of business hires.
Many pastors will do very low cost weddings on location or in their home or yours.