To wheedle is to sweet talk, or flatter someone in the hopes of getting something in return. You might try to wheedle a meter maid into not giving you a parking ticket. Good luck with that.
If you want your parents to do something for you that they don’t want to do, you may have to wheedle them with breakfast in bed and a shower of compliments in order to get what you want. To wheedle someone is to “charm” that person, though it’s a little more on the “suck up to” side than it is charming. The teacher’s pet might try to wheedle her way into a better grade.