I happen to stumble across a universal case from Targus that the Axim fits in nicely, and it's only $9.99.
You can find out all the particulars here.
Targus Universal Slip Case
It's not the greatest, and no it doesn't have any slots to carry the extra battery, but I'm able to put my Ax in it, and still carry my 4 in 1 stylus also. The flip cover is secured by velcro, and so is the belt loop, or clip as some call it.
Hope this helps.