I want my sister to design a tattoo for me without charging me
Why do you want your sister to design you a tattoo without charging you?
Because I love her with all my heart, but don't want to pay for the design of the  tattoo either.
If she is taking the time to design the tattoo for you, she should be compensated for it. Even though she is family, it is the right thing to do to pay her for her time and talent.
I don't care, I don't want to pay her
How would you feel if it was the other way around and she didn't want to pay you for something you did for her? I think it goes a long way to take good care of the people who do nice things for you.