From my googling so far, it appears that jade did not reach Ancient Rome, and classical Latin has no word for it. Possibly Pliny mentioned it in the Naturalis Historia, but he mentioned a number of green stones and it's not clear that any of them are jade. So, you're going to have to settle for Latin from a later time.
Normally a good first place to look for an established Latin word for something unnamed in Ancient Rome is Vicipædia, but Vicipædia has no article on jade.
If Isidorus of Seville mentioned it in the 7th-century Etymologiæ, it would be in book XVI, de lapidibus et metallis. I haven't checked thoroughly, but Isidorus does not appear to have mentioned jade, though iaspis might be a term for a broad category of green stone possibly subsuming jade. However, iaspis is almost certainly better translated "jasper".
As far as I can tell, Marbode's 12th-century De Lapidibus doesn't mention jade.
You sure picked a hard stone!
Possibly one of the earliest people to write about jade in Latin was Friar Odoric of Pordenone, who encountered jade on a visit to China in the early 1300s. From his travels:
in medio autem palacii est pigna quedam magna & alta passibus prulibus* quam duobus que tota est de quodam lapide preciosso nomine merdacas. & est tota auro ligata. & in quolibet ipsius angulo est serpens de auro, qui verberat eos fortissime.
My attempted translation, aided by Berthold Laufer's Jade: A Study in Chinese Archaeology and Religion:
In the middle of the palace is a big jar more than two paces high, made entirely of a certain precious stone called "jade". It's entirely lined with gold. Inside every corner of the jar, there is a dragon of gold, which attacks [them?] most powerfully.
Laufer believes that merdacas is a corruption of the Mongolian erdeni kash, meaning "precious jade". I didn't find any other uses of merdacas except to tell the story of Odoric's journey.
You might consider the etymology of jade. It comes from the Spanish piedra de hijada, "stone of the flank", so named because native Americans told the Spaniards that jade is useful for curing diseases related to the kidneys. Rewinding this back to Latin, you get petra iliata, though iliata is unattested.
The Latinitas Recens offers petra nephritica, using the Greek word for kidney.
*I'm assuming that prulibus is a misspelling of pluribus.