My wife and her aunt just had a conversation about this recently. It boiled down to this phrase in the end: "That's not going to work for me." Whenever she has to tell someone "no" and knows they're likely to argue, that's the answer she gives. When they ask why, she just repeats it until they realize that the answer is obvious but would be rude to say.

Personally, I think it's still rude, but it works for her in ways that being bluntly rude don't.

I had a manager who told me for about a year straight that I had to stop telling people "no" so bluntly, but instead offer other suggestions for their problem. She said I was just shutting them down, and they ... felt bad or something. I forget what she said. The point was that I shouldn't just shut them down, but I should try to help them with their problem.

This was so hard for me to learn because when I ask a question, I really do want the answer to that question, and it infuriates me when they dance around it or try to guess what question I really want to ask and answer that. Newsflash: That was it. I'm very literal.