As a PhD-Advisor: How do I discourage a student from continuing? I know it is slightly controversial, but I am supervising a student who started with the right attitude, but is now less and less engaged with the research. We are at a point where there's no end in sight, and the student still wants to finish within unmanageable time limits.

The context is peculiar (but I would like to keep it detached from the generality of the question): he's a part-time student, he's paying his own fees (as opposed to a PhD funded by a project), and he's after the PhD "title" more than the research that he has to put in for the title itself.

All these factors make it more difficult to dissuade him from his PhD choice: the endless excuses of putting more work when there will be time (he's a part time student); and the fact that I am proactively chasing him to arrange meetings are all things that are taking their toll.

My (general) question is therefore: how do I dissuade a PhD student from wasting his time and money, when it's clear that she is not PhD-material?
Do you want to dissuade the student from continuing because


You think the student is not capable because of a lack of ability,
You think the student might be capable, but just isn't engaging in the work,
You don't see the student is worth investing your time in,
You think the student is wasting his/her money?


If (1), then a frank discussion might be the best way. I have seen other PhD supervisors directly let their PhD students know that they think a research career is not for them. 

If (2), you ought to move from dissuasion to a frank discussion in which you try and figure out the reason for the downturn in engagement. Is all well at home? Is it just the usual mid (?) thesis malaise? Has the student lost the big picture and therefore the drive to do the research? Why did the student start the research in the first place? Has the situation changed - e.g. has the life goals been redefined/changed?

If (3) and/or (4), if the student is  paying for themselves, then it's their money they are potentially wasting so I wouldn't concern yourself on how other people spend their money. However, the money is presumably paying your salary in part so your obligations to the student remain in that regard. In return however, you can set reasonable expectations on your student. If you make it clear that you expect your student to achieve reasonable goal A by reasonable deadline Z, and the student doesn't, then that opens up another opportunity for a frank discussion along the lines of the need for effective prioritisation of research work and for-money work.

EDIT: To bring this answer into line with the edited question, I would set out an agreed plan of work - and behaviour (esp. showing up to meetings) -  with deadlines for the next 2/6/12 months. You might want to work with your Head of Department/School on this to ensure that your requirements are reasonable. It appears that you have already said to the student that in your opinion the student isn't PhD material. In setting out your agreed workplan, you are giving - formally - the opportunity for the student to show that he or she is capable of working to an agreed standard. If, as you say, the student isn't capable, then the student will fail and you can reasonably excuse yourself as his PhD supervisor. 

I am suggesting this cautious approach, as I am sure your Faculty will want to know why things went this way, and that you offered the best opportunity for your student (or fee-paying client) to succeed, before you ceased to be his supervisor.