Saying no to whom?
A boss can say yes, no, I don't know or I know but can't say. If the answer is 'no', then so be it. If the answer is honest and appropriate, a simple but dignified response is usually best received. Absolutely no lying as justification.
In non-work situations, a similar approach but with a bit more explanation for children. Again no lying.
As we all have learned, 'no' is a legitimate and common response. Live with it.