Off the wall thought....what if you set up your jewlery the way you want it with lighting, etc....then place a mirror in the right place and take a picture of the ring in the mirror? You would then be taking a picture of the opposite side of the ring, and shouldn't get the reflection from the camera.
Also, you could place the camera at an oblique angle, so its refelction was at least mostly bouncing away from the lens.
I see you posted as I was typing....you've got some pretty sharp highlights from your light source there. They also look underexposed. Try absolutely blasting your flash at that thing, and fire it through a diffuser like a soft box that is much larger than your subject, or bounce it off a piece of foam board. The idea is to make the powerful light come at the subject from every angle. You may then be able to overpower the reflection of your camera.