Since you are thinking of calling her My Precious Gem and calling her Gem for short, I did a search on yahoo and found this:
Gemstones are classified into different
groups,
species, and
varieties. For example, ruby is the red variety of the species
corundum, while any other color of corundum is considered sapphire.
Emerald (green),
aquamarine (blue),
bixbite (red),
goshenite (colorless),
heliodor (yellow), and
morganite (pink) are all varieties of the mineral species
beryl.
I like Bixbite and you can call him Bixy for short. Or Lapis (which is a blue colored gemstone) Those sound a bit more masculine. Most gem names sound feminine (pearl, sapphire, ruby). Good luck!