Cool, your Bonnie looks just like mine, but mine is an Purple SSEi. But I have the Bose system you have.
The rear speakers are AC Delco speakers made by Bose. They are a Dual Cone 6x9 as used in other Bonnies, but in this Bose model, they run both cones off the same amplifier output. You also have a tweeter built into the speaker grill.
So theoretically, this is a 2 way speaker system, but it does sound good.
The only issue is that the Bose speakers are paper and crappy at bass after they get a bit old. You may also be noticing crackling or a weird thumping sound. Anyway, its the speakers if that happens.
It is quite ok to put new 6x9 speakers in the back. Most brands will fit and Crutchfield has a good selection, including free harnesses and installation instructions.
I have plenty of information about that Bose system if you have any problems. Its a good system, just keep an eye on the paper coned Bose 6x9'*.