Styling Custom Bullets in BP-Corporate Theme

Quick question guys. What would be the best way to go about adding custom bullets for individual posts and pages? The key here is that I don't want to use the custom bullets through out the whole blog, only on a list by list basis. Other times, the default bullets are fine.

A typical use case for me is as follows... I have a blog page that I'm using as a squeeze page for a newsletter. The page contains two lists. "List 1" lists the key benefits, and I'd like to use "greencheck.png" as the bullet icon. "List 2" lists the shortcomings of other methods, and I'd like to use "redx.png" as the bullet icon.

Basically, I'd like to define a couple of CSS classes for lists (in my child theme, of course). Then, whenever I needed to use one of the two custom images, I could just go into the HTML tab of my page editor and replace:

<li>Key Benefit Number 1</li>
with:
<li class="greencheck">Key Benefit Number 1</li>

I'm just not sure how or where to properly define the classes and haven't had much luck with trial and error. Of course, if there is a better way to accomplish the same thing, please let me know.

The blog is running BuddyPress Corporate 1.3.8 on WordPress 3.2.1.

Many Thanks