You are capable of happiness. If you want to test this for yourself, think of something that you enjoy. If you could think of something, that is a bit of happiness. If you could think of nothing, then it is really important to believe that you are capable of happiness.
Happiness is the flip side of sadness. You cannot feel one without the other. When you get stuck feeling sad, it is important to remember that happiness is possible. You can see it in other people, but you think that it is out of your grasp. It is not. By feeling around inside your sadness you can find small pockets of peace. You also have your senses. You can see beauty, you can smell comfort, and you can feel warmth. Any pleasant sensation is a drop of happiness.
If you doubt you ability to feel happy, just feel for bits of happiness. They are everywhere.