Ah right, well if you want to be able to run your stereo for longer with the car on accessories then you can buy a bigger cranking battery. Obviously not so large you can't fit it in the engine bay.. But the bigger cranking batteries will allow you to run the stereo for longer without flattening the battery or having to resort to a dual battery system.
You can't put in a deep cycle though because that type of battery won't be able to start the cars engine.
Other things that might be worth looking at is the electrolyte level in the battery (if it isn't a sealed unit). If it has little screw open things on the top, then you can check the level of the fluid, top it up if needed with deionized water. Theres nothing wrong with the shop battery though, if its not broken its waaay to expensive a part to be replacing for no reason.
have fun