My suggestion is to use manual focus, manual shutter and aperture. Use the remote control software part of the package that came with the camera to compose the image on your monitoR and not the back of the camera. Also use the shutter release from the computer and not the camera as it is inevitable that you will create camera shake.
Use the smallest aperture for maximum depth of field as it is very limited at close range.
Keep the mirror locked And ensure a firm tripod is used.
Once you have the composition on your monitor, place small white cards around the subject to get the desired effect with the reflected light, all whilst managing from your monitor.
Try not to mix two different types of lights, that is, natural and spot light as they are different kelvin and will make your jewelry look different to what it actually is.
A glass table with a white sheet of paper with a light underneath will provide a great white background with no shadows.
A white card at the 5 o'clock position to take away the shadow next to stone and a black card at the 10 o'clock position to bring back depth will help greatly.
Once set up is done, ensure you have secured all the reflectors from moving and now you are ready to photograph all similar jewelry without any further rearranging. Ie, rings.
At a more advance stage, you can also consider, photo stacking.