I'm a freelancer, and with that, I get a lot of people trying to take advantage of my time. If I can't do something, they want to know WHY I can't do it, or if I'm scheduled to do something else at the time. Quite frankly, sometimes I'm not scheduled to do anything else--meaning I don't have any appointments. That doesn't mean, however, that I don't have any work, and if I didn't make time for my work, it wouldn't get done.
I've always had problems with, "No, sorry, I can't make that," because people always follow up with: "Why, what are you doing?"
I've found a really great impersonal statement that seems to stop all questions: "My schedule won't permit that."