I don't have a plugin to recommend but you could do this yourself by editing your current calendar plugin to use a month-specific image in place of whatever image code it's using at the moment. For example:
$calimg = "http://www.yourwebsiteurl.com/images/".date('F').".png";
Would that code work as printed there? I don't know. You may need to 'echo' the <img> code. I can't remember off the top of my head because it's been a while since I coded anything for a WordPress site.