I was wrong. Still can't figure out an adequate solution. The :nth-child(n) approach doesn't seem to work for nested categories, because when the user clicks on a parent category on the Forums page to view a category, the first subcategory is in the same position as the first parent category on the Forums page (e.g., :nth-child(1) on the Forums page selects the first parent category, but it also selects the first subcategory of the parent on the category page).
I also tried to use img[alt="CategoryName"]::before to insert Font Awesome conent, but that doesn't work on the img tag for most browsers. Unfortunately, the <a> tag that contains the category name does not contain a unique class.
Finally, I tried to insert <i class="CategoryName"></i> before my category name in the admin backend, but the html gets stripped out when I save it.
So if anyone knows of a way to use Font Awesome for category items that will work consistently across all views for categories and subcategories please let me know.
Thanks again