I see two options:
1. Display your ink
2. Cover it up with makeup and stencil his tat over it
Depending on what your tat is of, I'd say to just go with your own ink. If anyone has a problem with it, that's their problem. It'll be less screen accurate, but will likely look better, especially if you don't have experience covering a tattoo.
If your tattoo is of something that wouldn't work with the character, or if you wanted to be totally screen-accurate, then get some tattoo cover-up (I'm sure there are tons of tutorials and products for this, look around the makeup forums and online for tips and reviews), and then stencil the new one over it, probably with something like a cream body paint (Ben Nye or a similar brand), powdered and sealed, since a water-based paint would probably either not stick to or mess up whatever kind of concealer you use, depending on the formula of the tattoo concealer.
(Japan Expo 2013) Callisto Yew (Ace Attorney Investigations)
(SacAnime S2013) Fancy!Grimdark Rose Lalonde (Homestuck) ♣ Ballgown Dreamer Roxy Lalonde (Homestuck) ♠ Midnight Crew-inspired Alpha!Rose Lalonde (Homestuck)
Original design!Kanaya Maryam (Homestuck)