Practice makes perfect. Make sure you run through what you're going to say. Get it clear in your head so it doesn't come out in a garbled fashion.
Give your reasons. Don't try to soften your rationalisations in fancy language or coat them in sugar. Be clear on why you can't help. The clearer the message, the more likely it is that it will be understood.
Ask questions. Listen, and give the other person the chance to air what they think and feel.
Acknowledge their situation. Stick to your guns, but show that you understand - 'I know you are very busy with work and the kids, but I'm sorry, I can't help out this time.' It is emotions rather than facts that tend to make saying no difficult.
Reassure them. We often take a rejection personally. Be sure to show specifically why you need to say no and confirm that it doesn't mean you think any less of them as a person.
Own up. Have you created unrealistic expectations? Take responsibility and clarify the situation. If the truth is that you're short on time, tell them. They will respect your honesty.
Offer constructive options. Suggest possibilities for the future, but make sure these are realistic. If the candidate isn't right for the company, don't close by saying that you hope your paths cross again sometime.
Play the long game. Don't worry too much about their immediate response. They may well be upset at first, but they will come round in due course.