Hi,
If you just want to make a negative 12V supply to be used with the 12V positive supply, a bridged amp (two amps, driven out-of-phase, and a speaker connected between them) effectively doubles the voltage for up to 4 times the output power than a 12V amp.
Most car radios today use that technique, and you can buy it in a single cheap and simple IC.
I bet your car radio (if it is fairly new) already has amps like that. Your problem is probably that the cheap speakers are 20 ohms and therefore draw only 2.8W.
Most car radios can deliver between 14W to 20W (depends on the supply voltage, 12V to 14.4V) RMS per channel to a good 4 ohm speaker.