I used this tutorial: http://simswiki.info/wiki.php%3Ftit...a_Sims_3_Tattoo
When I finished I ended up with it being the wrong colors. It was blue and yellow instead of blueish grey and red. Also I got a black background around it.

The black background makes me think there's a problem with the alpha channel. On the alpha, white = opaque, black = transparent. The colors on the other channels can be whatever else, it's this channel (Alpha) that tells the game which parts of the image to show and which not. Also, make sure you save your image as a DXT5.

For the actual tattoo, clone an accessory that's basically a painted nude body (e.g. those red gloves), and replace its images with your tattoo's.
If you want your tattoo to be recolorable, make a black & white diffuse (main texture, should look grayish), and an RGBA control (with red, green, blue, yellow/alpha for any channels you need; leave the unused ones complely black).
If not, you can just paste your already-colored image as the diffuse and control, though that will make the game still recolor it to some degree as it still reads RGB info from the texture.