It might be quite challenging persuading someone to do something he is not motivated to do because, his failure to see a reason to do it is the first hurdle to be crossed.
In that case, I would suggest you have a good understanding of that thing you're asking him to do this would help you talk about it with authority. With that, you can tell him of the benefits inherent in doing it and the possible dangers of not (if any).
Alternatively, you could try to get the main reason(s) why the person doesn't want to do such thing, with that it's also easier to get ways to counter it and encourage him to.
You could also offer to lend a helping hand. Maybe him seeing some on to do that thing with him would encourage him to do so.
I hope this little helps.
One of the easiest way to persuade someone to do what he/she is unwilling or reluctant to do is to let them know what's in for them should they do it. If you can let the person see or understand what they will benefit from whatever you're trying to persuade them to do and the benefits are tangible, they will do what you want them to do without any hesitation.
Present the benefits in what you want the person to do in a way that it will stir a desire in the person. If you can do that you won't have any problem persuading him or her to do what you want
Are you trying to sell something to someone? Haha. Why would you want someone to accomplish something they don't like to do? Is it because they are getting fat or are smokers?
We really cannot change other people (unless you are raising kids, that's different). We can only change ourselves. I am not pro-changing other people when they do not want to do it. If they cannot realize the need for change for themselves then they will never change no matter how much you tell them to. Even if you keep telling them or plead with them, they will revert back to the way they were before. The only way to do it is if they experience something that will make them change their minds.
For example if someone suddenly get the cancer scare, they will begin to live a healthier lifestyle afterwards: stop smoking, stop eating junk food, etc. Or let's say they got into an accident, they may become nicer or cautious people or even be safety checkers. Those are the extreme measures though. One can always suggest to someone why they should do something but do not expect they will do it because if they don't want to then they won't do it.
Think about it, the same goes with you. If you don't want to do something and someone is trying to persuade you to do it, would you like it or not?