You can do this within the category settings:
Magento Admin -> Catalog -> Manage Categories -> Custom Design -> Custom Layout Update
This section takes XML updates, and you can add CSS to your head via XML here, like so (choose one):
//Simple way for CSS - Falls Back from Your Theme to Default/Base
//Goes to your theme's skin folder first
<reference name="head">
<action method="addCss"><name>css/yourStylesheet.css</name></action>
</reference>
//Specific way for CSS, can also be used for JS
//More lines, but you can change the type for different folders and javascript too
<reference name="head">
<action method="addItem">
<type>skin_css</type>
<name>css/yourStylesheet.css</name>
</action>
</reference>
Save and refresh your cache. Make sure your stylesheets are in the right folders!
addItem Types
<type>skin_css</type>
=> Magento/skin/frontend/your_package/your_theme/
Folder
<type>skin_js</type>
=> Same as above, specify folder js/yourScript.js
for name.
<type>js</type>
=> Looks in the root Magento Installation Folder. Used for the "\js\" and "\lib\" folders in the root directory of a magento install, commonly. I suppose you could tree it out to different folders if you'd like, since the base magento directory is the working directory with this type.