I don't have any tattoos, but when I bought the brand of makeup I currently use, the cosmetician told me it works wonders on covering up tattoos. She showed me pictures of some cover ups she did with the makeup on herself and on clients, you couldn't tell a tattoo was ever there!
The makeup is called Cover FX, its made in Toronto.
http://www.coverfx.com/
I have fairly sensitive skin too (thanks to going on Accutane for 3/4 year -_-), and this stuff is great for me; doesn't make me itch, the cream-based cover up is light and keeps the skin soft and moisturized, it doesn't smear, etc.
Check out the site. I got my Cover FX at Shoppers Drug Mart (Canadian version of the US Drug Mart Walgreens)
Though, this stuff is quite expensive. Mine has lasted me a year though because I don't have to constantly re-apply, and only need just a little bit to actually cover up. :P