biggest rims that will fit on a 2009 cobalt coupe

It will fit at least a 20" rim without modifications.

...with some minor clearancing of the spindle a 20" will fit. The real question is do you want it to ride like its going to...

...with a 30 aspect ratio and full insurance of your wheels for when you bend one from a minor pot hole.

I have a 225/45r17 and it rubs and has shredded my inner fender walls with only a .5” drop springs