First of all, keep yourself in hand. It is clear that the nerves are on edge, it seems that parents just rested, and I want to snap and be rude. You cannot do it! Better, on the contrary, to appease the parents, "sucking up". Mom probably see through this trick, but her loving heart couldn't resist.
Works well comparison. Give an example of what the friends have long been what You also want to have that You don't want to be worse than others. What kind of parents want their child looked "black sheep".
You can convince mom and dad to agree by convincing them that they are even profitable to buy You what you ask. Or to give permission for the trip. To find the powerful arguments, mentally put yourself in the place of parents and think about what arguments they can to sell on.
If previously these parents promises always been the case, offer in exchange for their agreement to do something. For example, to improve grades or help around the house. It is clear that the promise will have to perform, otherwise at other times parents just won't.
To persuade parents to allow you to stay away, to go overnight camping, stay the night with girlfriend or boyfriend, find someone who can vouch for You. It should be a responsible person whom the parents trust.
And finally, if nothing happens, then patience is the key to success. Look for the weakest place of the parents to take new attempts at a time when they have a good mood. The chances to persuade mom and dad will increase significantly. And luck will smile!