Do you mean something like this :
I setup my forum with custom ranks based on post count, but instead of ranks they are Levels. The first image is the Usergroup image, the image at the bottom is the user Rank Level. I custom coded my postbit legacy just for my forum though, so that feature its not in vBulletin by default. But if you need help with the code, I could help you. Just let me know.
In your case you could change the levels with your own images.
I am not sure what you mean by you don't want the ranks to be based on Post Count. How do you want them to work or increase in rank? If you just want only a few people in a usergroup to have a specific rank/badge image, I think the only way to do that is to edit the users rank yourself via AdminCP. As far as I know anyway, but I could be wrong.