I have DNN Professional on one server, where I am hosting 2 different sites.  I want to be able to customize the feedback and search module for each...I want different styles for each.  How can I do this?  I understand the hierarchy of css in DNN, but the core modules seem to only have the ability to have one style applied to them, in module.css.  Is there a way for me to style it differently for each site?  
Thank you.

Thank you everyone for your posts.  I took a lot of styles out of module.css, as I need the modules to be stripped as much as possible, and they now reside in the different skin folders in skin.css, which is what I wanted anyway.  I have been working with a skin that had already been developed (I thought this would save time).  It had a lot of inline css code which I removed.

Now I am able to customize the feedback module through skin.css, which is what I wanted.

The search module is different, however.  I want to be able to use different search buttons for each individual website, but it seems to only allow one.

It seems that editing portal.css would overwrite all styles in the site, am I correct.  I have one dotnetnuke portal with 3 different websites on this portal, all using 3 different skins.  This is where the problem lies for the search button customization between all 3 sites under one portal.

Any ideas on how I can make 3 different search "go" buttons for 3 different skins, while residing under one portal?

Thank you,
Gina