Can’t say much as far as getting an aftermarket cushion. I do however know you can buy the covers in whatever material you want by several aftermarket companies. And no, not the cheap crap that just wraps around your existing fabric.
As far as cushion replacement goes, you of course need the seat to be removed from the car. You’ll possibly need to unfasten the seat back, but possibly can get away without doing so.
The seat fabric comes off with fasteners call hog rings. You’ll need to bend them open with pliers. Sometimes good to have a couple pair of pliers, one to hold the hog ring, and one to bend them or squeeze them back into place. It’s easier to remove the fabric on a warm or hot day, so I recommend removing the hog rings first then leave the seat in the driveway so the sun warms up the fabric making it easily removable. Also be aware you may have an occupant weight sensor under the fabric so be mindful not to cut wires or fold the sensor pad. If there’s a sensor pad it needs to be installed back into the same spot for proper function.
I can’t exactly say I remember how the seat cushion is attached on the Cobalt but I believe the internal springs are what holds it to the seat frame with hog rings. Basically the same way as the fabric attaches.
You will have to likely source the seat cushion from a car from a junkyard. In this case finding a good cushion will likely mean you’ll be finding an entire seat that’s in better condition than yours, along with the fabric. I know the Pull-A-Part junkyard here where I’m at sells the seats very cheap. So you may be better off with an entire seat. Although if you remove just the cushion and cover, and get those alone, it is a bit cheaper than buying the whole seat.
I was considering getting new seats for my Cobalt. Mine are light grey, and being a mechanic, they get very dirty even when I’m fairly careful to stay clean at work. I have seen my customers cars with the same seat material, and these just seem to get extremely dirty for some reason. Anyways, I wanted to get different seats in the darker grey or black. But haven’t done so yet. I was thinking of putting the seats I have from a Honda Prelude in as they are way more comfortable. But will have to modify the brackets.