The style of the message will depend on the template that is being used.
View the source of the page when the message box is displayed. Find the message in the html code and look at the styles that are used. Then go to Merchandising > Custom Templates > Shopping cart and use the Copy ShopSite template to find the Template used for the theme you are using. Make a copy of that template and then edit the template and see which style files are included in the template (or perhaps the styles are defined right in the template.) If there are include files for the styles make note of which ones are used. Then go to Merchandising > Custom Templates > Includes and find the include files that are in the Shopping cart template and copy those include files. Look at each include file to see if it contains the style that is used on the [-- ShopSiteMessages --] in your shopping cart. Once you have found that section modify the style to meet your needs. After you have made the modifications and saved the file use the Copy button to copy your file and give it the same name as the ShopSite file you copied it from. This will allow your file to override the ShopSite provided include file.
Note you might be able to find what files are being use by going to
http://www.shopsite.com/templates/cookb ... ates.shtml and find the template you are using and clicking on the link to see more details about the theme. Usually there is a list of all the files used by the theme so you can pick the .css files and in the backoffice just look at those include files.