If you want to use an official item, there is the "Insignia of Claws" which can be found in the HOTDQ. From what I remember it gives a +1 to hit & dmg for unarmed and natural attacks.
I'd rather just let monks use monk weapons with their martial arts and flurry. Simpler solution and allows them to use a wide variety of options.
You can roll a d4 in place of the normal damage of your unarmed strike or monk weapon.
Note that this is RAW. Your phrasing doesn't make it perfectly clear.
Martial arts says:
I believe he's referring to the bonus action attack(s) granted by martial arts and flurry, which are normally unarmed attacks, and not to the damage of monk weapons.
This is exactly what the rules tell us.I find it hard to believe that allowing three to four strikes with a +1 magical weapon is broken, but allowing two strikes with a +1 magic weapon and one to two strikes with +0 magical unarmed strikes is perfectly fine.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.