Yeah, the problem with the image is the colors area actually very close to the same tone and the differences would be pretty subtle when lasered. Like elfguys suggested, your choice is to recreate (or download them for cheap from Etsy) a vector file and then adjust the colors in them so they all look different, or try and adjust the tones in the bitmap version.
I did a quick example to show how adjusting the bitmap might work to give things some contrast between each diamond. It just might be something you have to play with and test a few times to see what works best. (This probably needs some more work, but it gives you an idea what might work.)
Here’s some Etsy links if it’s easier to buy them.
FWIW, I found a higher resolution PNG that was better to work with.