Outline your idea. Think all of the arguments against your idea so that you're prepared to counteract them. List reasons for the change or idea for the team. Be prepared before you attempt to persuade.
Speak to the supervisor of the team. Don't present a change without making sure that the administration will support it. Don't complain that the team doesn't agree or will be resistant; rather, bounce the idea off the supervisor.
Meet with the individuals on the team. Persuading an individual can be easier than dealing with the whole team at once. Talk to each member without being too forceful. Listen to each complaint or concern that a member may have. If you're not willing to listen to others, you will never be able to persuade them. Use your list of counterarguments to convince each member.
Determine who supports your idea and who resists it. Try to set up another time to discuss the new plan. Some people take more time to get used to something different and rushing change won't help persuade someone who doesn't initially agree. Continue individual discussions until you have the majority of the team's support.
Meet with the group as a whole. Start by asking if you can have a moment to outline your idea. Let the argument or idea speak for itself. Try to avoid using "I" and stick to the validity of the idea itself. Answer questions as they arise without becoming defensive.
Follow up with the team. Find out if the members feel that the change was effective. To be truly persuasive, you will need to admit if an idea wasn't successful so that next time the team will respect your opinion and trust it.