It's hard to imagine you not getting fire shots with that diamond of yours!!!
I don't know..I'm just going to sound like a big photo nerd if I go into it..lol. First off I have no idea how to get a fire shot with a point and shoot, but then, I've never tried. If you have a DSLR, one key is to raise the aperture as high as possible. Same is true for sun flare. You need a high f stop (ie f18 or higher) to get nice flare. I think my ring shots were taken around f29, partially because I'm using my macro lens, but also trying to catch the fire's "flare".
Another part is just to move slightly till you see the fire and focus and shoot. But once again I'm using a dslr looking through the viewfinder, so what I see is what I capture. If you are using a point and shoot this isn't necessarily the case.
With a point and shoot I would say make sure the iso is as low as possible (if you can adjust it) which will help the camera shoot more closed down (higher apertures). Use the macro setting and fire away like mad just adjusting your position every so slightly...like only millimeters of movement.