This still puts the 'requestee' in a bind. Why should s/he have to think-of/figure-out an alternative? The requestor should be able to take a "no" for an answer and not feel entitled. Of course gentleness and politeness (usually) go a long way in making it easier.

Yes, always be polite. I find if you give some reasonable alternatives, they often take one of them. Sometimes you need to let them talk a little more to find out really what they are trying to accomplish and what the priorities are.

I have incorrectly assumed that time or money were the priorities, but with a little more information found out something else was really driving the request.

Sometimes the person making the request is entitled - they're in a management role and they're giving you a task. In that situation it's a good idea to show that you would do it if you could, but at the moment you can't. That allows the manager to do their job (assigning priority) and makes it clear the decision to reassign work was theirs, not yours.