No one likes to be left hanging. When you say no, give the requestor another option. It’ll go a long way toward mitigating his or her disappointment at your inability or unwillingness to lend a hand.
If you’re currently helping the requestor with another task or project, options can also take the form of an either-or decision. For example:
John, I’m barely keeping my head above water helping you with Project ABC. I can continue to help you with that one or help you with this new one. But not both. Which one would you prefer me to work on?”
This approach doesn’t only work in an office environment. It works with friends, family members, neighbors, and even strangers. By offering the requestor an alternative, you’re showing him or her that you care. You’re also lessening the requestor’s disappointment at hearing you turn down his or her request.