Ok as someone who's pregnant and has 26 hours worth the tattoo work. I'm going to tell you exactly why you MAY not be able to be tattooed. (I didn't really read all the replys so if these have been stated i apologize)
The first reason is if you're showing a credible tattoo artist will refuse. More to protect their own butts then anything.
Second reason and this is the MAIN reason. Guess i should have put it first...
Getting a tattoo (or piercing) causes trauma to your body, it gets adrenaline running speeding up heart beats, blood flow, breathing. Think of rollercoaster rides, you can't go on those when your pregnant and its for the same reasons.
A properly done and cared for tattoo has as much chance of infection as an open cut on your hand.
It's true woman do get tattooed and their children are fine. It's all just potential risks but what you really got to ask yourself is do you want to take that risk?