Sterling silver ring question?

Okay, so I have a sterling silver ring with letters carved in the ring and then the carved letters are filled in black. The black has worn off but the carved letters are still there. Is there anyway that I can paint the black back into the carved letters? It's very small, delicate, cursive letters. And the people I got the ring from aren't around anymore so I was wanting to do it myself with a small paint brush maybe? If you could please help me It's my boyfriend's promise ring and about 90% of the letters are gone. It would really make him happy. Thank you in advance.