They receive a letter grade for the class. It is participation based, and they have to demonstrate a few basic things at the end of the semester.
You have a fundamentally simple solution: Use positive and negative reinforcement to encourage change. When they try, recognize it and encourage them. When they slack, ignore them. At the beginning of class, remind them that their grade is predicated upon their participation in the class – if they fail to participate, they will not pass. This isn't mean, it's fair.
You, though, have to change the way you view your students. Keep your students at arms length until they prove their interest, and then reward them with your attention. Whatever reason they find themselves in your class, you have the ability to make them seek out your encouragement. This is by means of promotion, one-on-one training, or even invitation out to group dinners following a class. Napoleon Bonaparte knew the importance of a "bit of ribbon", and really this is all to which belts amount. Further, working toward the ends of social cohesion, most with the exception of the most antisocial (sociopathic) will strive toward being part of the social group in an unfamiliar and specialized setting (organic solidarity, Durkheim).
Remember that you're dealing with late-teens and up; essentially adults (though the younger crowd may still be trapped in the sociopathic tendencies of teenage rebellion). Show them respect, be friendly, but don't be a friend (at least not while you're still grading them). You're not going to engage everyone, but you can use the group dynamic to leverage the outsiders into the fold. Teach those who are willing to learn, and let them pick their own partners. Do not force the hard working, interested students to include or choose anyone they do not wish to partner with, which will further separate the outsiders from the group; they will then either a.) leave, or b.) assimilate.
Edit: New Subversion Tactics
It occurs to me that you have literally no excuse to be anything less than a perfect teacher. When a class is set on a schedule (that is, that it begins at the beginning of a semester, and it ends at the end), you have a finite time to create impact but you also have an audience that is captive to your message for a set period of time.
Ask yourself this: What makes a story work? There are, in every story, three parts:
The Invitation – The Hero/Heroine is introduced to the idea that everything will change. Dagny loses the railroad, Odysseus meets Athena, etc.
The Initiation – The Hero/Heroine is forced out into the world to seek a solution. Who is John Galt?
The Return – The Hero/Heroine returns fundamentally changed. Dagny leaves Galt's Gulch to return to the railroad as the government collapses.
We can break up a semester similarly:
The Invitation – The student must have a reasonable expectation set out in front of them. The student is going to learn Aikido and be able to demonstrate a functional capability to defend themselves from XYZ attacks. Failing to demonstrate that capacity is abject failure.
The Initiation – The student must be shown that it is possible, and be expected to demonstrate. Those that refuse will be failed. To succeed, they need to know that they are dependent upon your guidance.
The Return – Final exam time. What they have been taught they must now demonstrate. Much as the hero must succeed to return changed, so too must they succeed to pass the class.
The truth is that you are expecting results; therefore, you must expect them to deliver those results. Show them that you're willing to fail them. Welcome them to the real world where decisions have consequences.
I realize now in saying this, however, that your unwillingness to choose an answer exhibits the same attitude that brought you to ask the question in the first place: for whatever reason, you're unwilling to fail these students. You are accepting that your class is a class designed to be an "easy A". And that's not only disappointing, but shameful.
Have an ounce of pride and start out the way you mean to go: Invite the students to succeed or fail, and let them know that if they don't want to be there, they are invited to fail or find another class.