T.J.
I read a book once that said to never say no. You are, however allowed to say yes, with a time qualifier.
"Can I have a cookie?" "Yes, after dinner"
"Can I watch a movie?" "Yes, tomorrow."
I've never remembered to try it on a consistent basis, but it sounds like it might work better than a flat out "no".
That said, when the dreaded word "no" does make an appearance, followed by the predictable meltdown, I try to talk to my daughter(s) about how I know she's disappointed or sad and it's okay to feel that way, but that she's not behaving in an appropriate way and try to help her find a way to deal with her emotions. I'm big on trying to teach my girls how to properly handle their emotions in a healthy way, mainly cause I struggle with dealing with my own. Good luck with it! :)