As others have said here, look into replacing the speakers. I would however take it one step further and drop in an amp and a moddest subwoofer in the trunk (around 200-300w should be all thats really needed).
I did this in my 05 and it sounded AMAZING (and the shaker 500 is a bit better now than it was in 05).
I have 1000 watts feeding the two 12"s in my trunk now, which is complete overkill with the top up and somewhere between awesome and silly with the top down. Earlier I suggested a minimum of 500watts as the top, when down, sits between the trunk and cockpit, with a rather large area that absorbs the bass response.
But if you have experience with only 200-300 watts being adequate with the top down, then that is good to know.
When i put my system together, i figured it is always easier to turn down a stereo than it is to turn it up.
2012 GT CS Ingot Silver Vert, Edelbrock E-force supercharger with CAI and 3.5 Pulley, Tremec T-56 Mag, Accufab 84.5, Centerforce DF, Billet Yoke aluminum driveshaft, FRPP 3.73 Rear, MRT Performance H-pipe, Bassani axle backs, JL Audio sound, Edelbrock strut tower brace, JPC adjustable UCA, UMI adjustable panhard bar, KW V3 coilovers, Steeda heavy duty front mounts, Steeda rear LCA's, 20" Steeda Spyders with Michelin Pilot Super Sports, Steeda Big Brake Kit ....... it just keeps going.