There is an entire thread devoted to how to take good pics of diamonds. Admittedly, I haven't been through it, and just use my phone/tablet mostly, and take pics in a variety of lighting: indoors, outdoors, direct light, indirect light, etc.
A macro lens helps, even a clip on one for the phone. I went so far as to biy a 15.00 light box from amazon lol, but that is probably unnecessary for you.
Take various pics of it, including head on. Bring it outside in the sun, place it between your fingers (be so careful!! Diamonds can be jumpy), and get some sunshine shots-- Some morning light in the bathroom shots-- black background, white background. (You may actually want to do this as your fiancee will likely appreciate all the show off pics she can show her friends)... place it on a flower or a piece of fruit so the camera can focus...