In Hoard of the Dragon Queen, there's a magic item that gives +1 to unarmed attack and damage rolls called the "Insignia of Claws". It's not in the free downloadable supplement PDF for Rise of Tiamat, so you'd only be able to see it by buying the Hoard of the Dragon Queen adventure (or the D&D Beyond pack for that adventure).
But even without seeing it, it's at least evidence that there is something official out there that increases attack and damage rolls for unarmed strikes in the same way that a +1 magic itemweapon does, so you should be good to homebrew something similar (or just use that exact magic item).