Most modules use the same css classes because the usual goal is to have a consistent appearance across features, not a different appearance. A few modules do use supplemental css files but this is mainly to help keep the main style.css file small.
The easiest thing I can think of is to use different skins for different pages. The module on a page will use whatever skin is assigned to the page. You can set a different background color in each skin.
Hope it helps,