Organ donation is a very personal thing. Sometimes, religious beliefs may hinder someone from donating an organ. That said, sometimes educating people is the best course of action. By demonstrating how many people's lives can be saved, sometimes that is the best way to convince someone.
One thing is to make sure that people who DO want to donate their organs talk about it with their families. Even when people have signed organ donor statements, or noted it on their driver's licence, the family can override the decision. So making sure that the people who are already on board take time to convince their families that is what they want, is crucial.
I think the most effective technique for doing this is to give them a long string of examples of where organ donations have saved someone's life, or greatly improved the quality of someone's life. When they can see the positive results and the huge difference it can make, they might change their mind. If you really want to be persuasive, and I'm just saying this from a perspective of your goal of being more persuasive, find examples of kids who have benefited from organ donations. It has a more powerful impact.
I am not really sure that it is right to persuade someone to donate their organs. It is really a personal choice. There are many different reasons why people choose whether or not to donate their organs so this may end up being a very sticky subject to them. It is commendable that organ donation is so important to you though. Organ donations save thousands of lives each and every year.
Instead of trying to persuade someone to donate, I would share with them what you know about organ donation. People do not necessarily have to donate their entire bodies. They can choose exactly what they wish to donate. By sharing your knowledge of organ donation, you are helping to educate them and then they can choose on their own.
To persuade someone to donate their organs is a very sensitive mission. It is the individual's choice as to what happens to their body after they die. Some people may have religious reasons, so you must be careful in how you approach the subject. One of the best ways to encourage organ donation is to educate people on the number of lives that can be saved by one person. According to the site organdonor.gov, eight people can be saved by one person donating their organs. Those eight people may consist of children, single parents, or even relatives. The impact that one person can make on eight lives is a amazing. Setting up a meeting with someone who was saved by an organ donor would be very powerful to someone of the fence. Witnessing the gratitude and love of life would persuade me.
It would seem to me that the key element here is "persuade." In the end, the choice is ultimately the individual's and you might have to live with the fact that some might choose to not enter the realm of organ donation. Obviously, it might help to point out the fact that the potential saving of another person's life could be one of the most persuasive elements behind organ donation. The life one saves with the potential for donating organs could turn out to be one of the most compelling arguments for it. Enlisting the help of others in this might be of value, as well. For example, the great running back, Walter Payton, taped a series of public service announcements days before his death which encouraged people to become organ donors. Given his suffering from a rare disease of the liver, it was especially poignant. After taping these PSA's, organ donation in Illinois dramatically increased.