Best way to associate images with categories?

Problem: I need to associate 2 images for each category & sub-category, which will display outside the Loop. What is the best way to do this?

Background: I am working on a template where I display thumbnails and post titles in a grid view on the category pages: example here. I originally thought there would be only a few categories, and planned to hand-code category-#.php files, with no subcategories.

However, the category structure is now going to be more complex, and the category pages will display, in a grid view, thumbnails and titles/links for subcategories (all posts will be inside sub-categories).

I need to automate associating 2 images with category pages, so that a thumbnail and a larger image can be displayed, outside the loop, for each category and subcategory.

I have tried out several plugins, but the ones I’ve tried are either one-image per category (I need two; a thumbnail and a larger display image) or they only work inside the loop.

Any helps would be appreciated.