I have made one pendant for a guy a few years ago, who wanted a briar cabochon instead of a stone. I picked up some scraps from Skip's home shop, where he makes his pipes. I cut a section out from a piece that had been sandblasted. The whole thing was sort of plain, but he loved it. But, it has since been sent back to me for adjustment twice. I'm really hesitant about using briar now, because it doesn't take a friction setting very well, because it is essentially spongey and wiggles out of physical settings, and it doesn't take epoxy very well either, not for the type of abuse a pendant swinging around your neck would over the years, and especially not on a ring.
There are a few guys making watch bands out of wood, where the wood is machined out with CAD and then linked to make a sectional band with links. I wouldn't mind something like that made out of briar, if it were then sandblasted. Maybe even have the watch case machined out of it as well. But, I am not certain how long something like that would last.