Almrond

You will probably be best served with an industrial label printer, I used one while working in a grocery store to make tags. They come in toner varieties, so no thermal paper issues, and they are made to be portable. That being said, they are not at all cheap or simple. You are wanting to look into two companies, Zebra and Symbol, specifically at their mobile printers.

https://www.zebra.com/us/en/products/printers/mobile.html?page=1

To be fair, what you are asking for is nigh impossible without going thermal, and the reason can be summed up by one question: Where do you plan on putting the ink?

The problem wouldn’t be fixed even then. The jewelery companies have people convinced that the only diamonds that are worth it are mined from the earth by a real human slave. Fixing that problem has nothing to do with gemstones.