How do you handle unproductive team members?

Be nice.  Find out why they are unproductive.  If you ask them, the first answer they give will almost certainly not be the real answer.

There are only two reasons why somebody is unproductive:  problems at work or personal problems.  If its the first, it's your job to fix it.  If it's the second, it's your job to provide a constructive environment for them to fix it.  if they can't or won't, it's your job to fire them in accordance with the proper procedures.

it depends on you, what you exactly wants, if you want their coordination, give them easiest jobs, also appreciate their efforts.Use carrot method. encourage them to build a bright future for them by telling them real or manipulated success stories. spend some time with them, it does't means you open your weaknesses. by the time passes you will feel them as useful assets of yours. 

I feel you cant use another techniques, Some people have made their image like, if they are around, team members always used to be productive.