Having just come off a Carnival ship, I can verify that yes, they do have tatooing, but it's a temporary airbrush tatoo, that will last about 7 days. Prices vary from 7.95 to 9.95 depending on the size.
The Liberty had air brushed tatoos by the pool area. They had a special deal on the 1st sea day, get a medium or large tatoo, then on the last sea day you can get it refreshed or a different one for $10. as long as you don't wash over it or apply lotion to the area they will last for about 7 days, mine did.
Teresa and Larry
#36-Carnival Splendor 9/16/12
7 night Mexican Riviera
#37-Allure of the Seas 11/11/12
7 night Eastern Caribbean