I've seen artists either flat out deny it (after all, people's tattoos are walking advertisements for your work) or talk them into something else.

For instance, originally I wanted two swallows on either of my shoulders, holding a banner in their mouths which would stretch across my chest. Instead, the artist drew my actual chestpiece (http://img.photobucket.com/albums/v511/cherrymaggot/tattoopictures001_editedSmallmod1.jpg) which looks a lot better.