A simple option would be to put an animated texture on a plane and parent it to the sword. Then, while in edit mode, select the plane, go to the editing panel, go to the texture face tab, and select halo (click copy if you have multiple faces selected to apply it to all of them). Let me see if I can put something together for you. I should have some kind of sword or other weapon model around here somewhere.
Edit: looks like it will take a little bit more tweaking than I originally thought, but I am determined to make this work in a similar fashion, especially since I have been wanting to do something similar for a lightsaber effect.
Dug up BGE lightsaber, but it the effect doesn’t work well with a sword in it. Also, are you looking for a lightsaber type effect? If not can you give me some details on how you want your aura to work?
I have here a demo file that has a plane tracking the camera (so it looks good from most angles) and still staying on the sword. It uses a python script that is fairly straight forward and is called track (it is located in the blend file). Using this you should be able to make a animated or video texture to get a good animated aura effect. http://pasteall.org/blend/244
The idea is not new and I finally found a thread that addressed this here. And I got help from the #gameblender irc channel to get the python figured out.
I plan to still do that flaming sword thing though, but it will be with fire instead of darkness. I will put up a link here when I am done if you like.
Forgot you were in texture face, so the particles on the flame sword will not work right for you. But on the aura thing, just go to the material settings, and change the plane’s alpha to 1, and turn of ZTransp.