How can I convince someone to quit?

There is nothing wrong with the person’s performance, so getting her to “move along” will not be possible by citing a lack of professionalism or expertise in her field. It’s just there is a good friend that I’d like to put in this person’s position, and this employee, even after transferring her to the most undesirable job area, and telling her we thought she would resign instead of move (you’d think she’d get the hint), after ignoring every request, denying leave (ignoring this person’s very existence at every opportunity), this individual just won’t “get it” and move along”! What can I do next to coax this individual to simply resign so we can fill the position with one of “our” inner-circle friends?