You can do this for modern browsers with a few lines in your stylesheet. Add to the end of your stylesheet.css
Code:
.productListing-data {background: #ffffff;}
* html .productListing-data {background: none;}/* IE6 hack */
.productListing-data+.productListing-data {background: none;}
This will not work in IE6 because it doesn't understand the adjacent selector "+", so the
* html hack will leave the background black for IE6 users only.
There is a more robust method available in the flexible product listing mod, posted in the styling product listing pages with column layout grid thread, post 50. The CSS-only version in that mod should allow styling for every browser.