I think it is comical that nearly 50% of Jets fans can't bring themselves to believe that the tattoo is even real:
OFFICIAL JI POLL: Rex Ryan Tattoo: Real or Rex Punking the Media - Jets Insider.com Forums
The other half have convinced themselves that it is a private matter and means nothing, as if it is perfectly acceptable to have an utter buffoon coaching your professional football team.
I can't even imagine what was going through his brain when he asked for that monstrosity.
If it's fake, I can think of two possibilities:
1 - A third party (not Rex or the Daily News) photoshopped the tattoo onto the picture and the Daily News assumed it was real. I don't know how likely this is. At a minimum, I would think, at some point, the photographer would see the finished article and notice the picture had been altered.
2 - Rex got a fake tattoo so he could embarrass the media if they followed him on vacation, took a picture of the tattoo, and made it a story. What's his motivation for this, though? So he can say he tricked Gary Myers and the Daily News? If that was the goal, then good job, I guess. I'd think a Jets fan would wish Rex put as much effort into beating teams in the division as he did in punking a reporter.
And if he was going to go with a joke fake tattoo, why not a TB12 or Tebow one, something that would be obvious that it was a joke? Why come up with something that's somewhat believable? Why bring his wife into it for no reason?
I don't think there's much of a chance that it's fake. If it's a joke by Rex, then his thought process behind it is so dumb that he'd be better off it was real.
[Edit: Just saw Joker's post and possibility #1 can be thrown out]