Well, we can make diamonds. Just need carbon and a lot of pressure.
As for other gemstones, well, their colours come from the various minerals, elements, etc contained within their crystalline structure. They tend to be not as hard as diamonds though so there’s not a lot of interest in creating them. Also, industrial diamonds, while incredibly useful for drilling and what not, are not as pretty as the ones Africans die mining for us. Sometimes, you can’t beat time and millions of tonnes of pressure.
As a general rule (if your chemistry is lacking), more reactive substances combine to form more stable compounds; two good examples are water and salt, both formed from highly reactive elements: Sodium, Chlorine and Hydrogen, Oxygen (elemental oxygen, not the oxygen molecule we breathe). Then, the more stable a substance, the more difficult it is to take it back to its constituents, hence why despite hydrogen being a wonder fuel, and water being full of it, and the world being full of water, it’s hugely expensive to get hydrogen from water because of the amount of energy you have to use to break the incredibly strong bonds in the H2O molecule.
Anyway, enough to be going on with…but it’s a good start in terms of understanding why some things are more stable than others.