On Amazon, I found an armband from a company called Tunebelt, its model "AB3". Nice and secure with my 8130, the top of the phone just slightly shows outside the pocket.
I was looking for a minimal design, and this fit the bill. Its not the most convenient since you have to remove your berry to change/browse music, but it is much more secure than some other styles that simply attach an armband to a rubber skin. I usually set the player on "random" or set up a playlist, and don't touch it while I work out or run.
Amazon link Amazon.com: TUNE BELT AB3 MP3 ARMBAND CARRIER: Electronics
Alternatively, body glove makes some universal styles that work, or you can look for an ipod case, I think the ipod mini is close to the same size.