Get to know them, identifying pro's and cons about their personality. Try to highlight the root of their depression, maybe even getting them to talk about issues which get them down. Take them out; introduce them to new social circles, let them know there are people out there that they can talk to and/or associate with. Congratulate them when they do something credible. Introduce them to types of music that relax and/or stimulate the mind. Try and make them spend more times out of the house. If they are unemployed, advise or even help them to get into a job. Believe me, unemployment has caused depression for me in the past and gets you so out of routine; you can feel like you're living an aimless existence. Introduce them to new hobbies; things to participate in instead of being alone with negative thoughts which progress into a depressed state of mind. If there's less time spent in introspection, there's a lower chance of prevailing depression. To be honest, I don't think it's a matter of convincing someone they don't have depression. It's more of a process of getting that person to face and overcome the issues that are making them depressed. Show them there's more to life; because it really is too short.
Maybe they don't have the so-called disease that is known as, prescribed as, and medicated as Depression. Maybe they're just in a depression, a mental rut, feel trapped in their life, sad a lot. Or maybe they're doing it for attention.... I don't know how you'd go about convincing them they don't have it. How do you know what they feel?
Why do you not believe this individual is depressed? Depression is a very odd human emotion that effects many people on different levels.