...depending on the headunit, you may be able to add a changer that will play CD-Rs... you may want to look into that, and maybe find one on ebay for $50 or so.

Older cd players dont have the ability to read through the darker coating on CD-Rs, and the only way around that would be to upgrade to a newer laser, but finding one that will fit and work properly would be an endless battle, chances are the only one that would fit and work, would be the same one thats in there. Even with the laser being new, it still wouldnt read the discs, it'd still be the same laser.

For $160 brand new, you can find a good to excelent quality headunit that will be capable of playing CD-Rs. This includes Alpine's entry level unit.

Depending on your car, you may also want to look into an OEM CD player... they can usually be had for fairly cheap, the sound quality wont be as good as most aftermarket units... but its just a suggestion, i'm not sure what your musical tastes are and how you like it to sound.