EEEK!
No. Never tumble anything of value in gravel...unless you want it to soon be nothing of value.
(Depending on the rock tumbler, a diamond can very easily chip...if tumbled in gravel.)
There are jewelry cleaning/polishing cloths impregnated with chemicals that will neutralize the tarnish and quickly/easily remove it.
They make them for both gold and for silver jewelry.
There are metal polishing pastes (such as Flitz) that can be used with micro-fiber cloths and a toothbrush to remove tarnish.
Tip: Be extremely careful with a micro-fiber cloth around the diamond mounts...the tiny fibers like to snag on anything and everything sharp.
There are household brands of 'old-school' liquid silver cleaner (such as Tarn-X) meant for silverware and jewelry.
Electrolysis works very well for tarnished jewelry, but obviously requires the hardware.
Hint: If you choose to try electrolysis, don't make the solution out of salt water...use baking soda instead.
If you think the ring is of very high value, take it to a reputable jewelry store and have them clean it for you.
Many well established jewelers will offer free (or very low cost) cleaning as a sales tool. Check around.
Finally, don't use any of these silver cleaning techniques on rare silver coins.
Anything other than very gentle removal of dirt with plain water, starts to degrade the value of a rare coin substantially.
mike