This is a common problem in the Sunfire, in case you didn't know. GM should have recalled it but they're not big on warranting anything (speaking as a never-again GM owner) Anyway...
Remove a problem speaker. Get a multimeter. Set it to read AC Voltage. Connect the multimeter to the 2 speaker wires. Play some music (for best results, I recommend Sepultura's cover of Procreation of the Wicked 'cause it's awesome). Does your multimeter respond? It should show a voltage changing depending on the music (ie. it won't be a steady xxx volts). If you get nothing, there's a problem with the wiring or the amp. If you do get a reading your speakers are likely the culprits. But I'm betting on wiring. To further diagnose you'll have to move on to your head unit/stereo. Leave the speaker disconnected while you do.
Pull the stereo. Disconnect the wiring harness. From what I can find online the color codes should be: Left rear speaker brown+ yellow-, right rear dark blue+ light blue -. Figure out which speaker you have out at the back (left/right is as when sitting in the driver seat). Connect the 2 wires at the speaker (just tape the connectors together if they're exposed, or use a little bit of wire as a jumper). Switch your multimeter to measure resistance. Check the resistance at the stereo's wiring harness between the 2 wires that go to your speaker. You should get a very low reading, likely well under 10 ohms. If you get a very high reading or infinity make sure that the wires are connected together at the speaker and didn't come loose. If they are connected then the wire from the speaker to the stereo is broken somewhere. I'm fairly certain this is what you'll find, considering what I've read elsewhere about this issue on the Sunfire.
If you find that you do get a low reading, meaning the wiring is OK, the problem is either in the connection to the stereo/head unit or the stereo itself. Spray some contact cleaner or pour a small amount of isopropyl/rubbing alcohol into the connector to clean the connections. Do the same at the stereo side of the connection (be careful not to put very much isopropyl in there - just use a q-tip if the pins aren't too close together). Reconnect the connector and the speaker and try Sepultura again. Work? If not, disconnect the connector and reconnect it a dozen or so times (this action cleans contacts). Try again. No Max Cavalera growling? Then it's likely the stereo is dead.
If you found earlier that the wiring was broken it's easier to run new speaker wire than to find the break. Unless you can find somewhere online where other Sunfire owners have found the break and fixed it (thus giving you somewhere to start looking) it'll probably be painfully slow trying to track it down. Running new wire isn't too hard. Any wire will do. Speaker wire/lamp wire (protip: it's the same thing but the speaker wire costs 10x as much) usually has 2 conductors joined together so it's easier to pull. I'd usually pull it under the carpet but however you want to get it there doesn't matter. When you get it up to the connector cut the old speaker wire off so that there's 6" or 8" of wire left on the connector and use a quality splice connector to join the new wire to the old. Don't try soldering the wire - not only is it hard if you're not experienced, soldering changes the impedance and varies it over time and should never - NEVER - be used for signal carrying cables on a vehicle. It will inevitably fail. All major automakers spec this for repairs.