On my 99 bonneville se the rear speakers will rattle (is that the word?) when a song with a lot of bass is on or when I hve the bass turned up. Is there any way to correct this without sacrificing the bass or replacing the speakers?

to be honest id say no, guessing its a stock system. factory speakers distort and make some weird nioses when turned up,bass and all and when ya turn the bass down the noise stops but bass is lacking. id recomend upgrading to aftermarket speakers to help solve the prob or just turn the bass down a lil bit til the noise stops.

Sounds like you might have a blown speaker back there. I guess it could be bottoming out too, or even a loose panel somewhere.

What would be a good, cheap set of replacements ( Is that an oxymoron? Lol)

How cheap? You will see an improvement with Walmart/Meijers Lighning Audio 6x9'*.. Look on sonicelectronix.com for better options tho