Run through what you are going to say in your own mind or with a sympathetic friend. Otherwise you may confuse the other person, which they might interpret as an attempt to deceive.
Be sure that you mean no before you begin and don't start to waver afterwards. Saying no at the beginning. makes it more likely that everything else you say will be heard and understood. It also shows you consider the other person as an equal.
Give your reasons. Say them straight rather than wrapping them in fancy language. The more tangible and specific your reasons, the better.
Show you care. It is emotions rather than facts that make saying no difficult. Show sympathy or empathy.
Ask questions, especially about what the other person thinks and feels. Listen to the answers.
Take responsibility for any contribution you've made to the situation - eg, 'I should have explained earlier'.
Draw positive broader implications for the individual. We tend to extrapolate from rejections what they say about us as a person: 'Has my pay rise been refused because I'm not worth it?'; 'Does Jim disagree because he thinks I'm stupid?' People accept rejection on a given issue more easily if it doesn't threaten their self-esteem.
Offer constructive options for the future, but only if there are any. Don't invent unrealistic ones.
If you're not loved immediately, don't worry. It may take time, and it may never happen. All you can do is try. This is about them as well as you.