OP, you've gotten a lot of great ideas!
When my twins would go on and on about something, I'd say "Do you think if you ask 10 more times, I'll change my mind?" Or, if they were actually throwing a tantrum about something (and the mood was right), I'd ask "Do you think if you yell and scream loud enough I'll change my mind? Go ahead, give it a try!" Encouraging them to throw a bigger fit was silly, and they knew it - but they would play along. A minute later I'd pause, concentrate hard, and say "Nope - the answer is the same". That worked in our house because if I made a decision about something, I stuck to it - no amount of whining or begging would get me to change my mind, and they knew it.