That's a very loaded question.
No, I don't believe someone can CHOOSE to be happy. They can however take steps to MAKE themselves happy. I guess sometimes people try to project images and thoughts of happiness, but I don't think that works, and it's just outside fluff. Many times, on the inside they're not happy at all, even though they try to act like it on the outside.
Sometimes you need more exercise and/or a better diet to build serotonin levels up. Sometimes you need a relationship, or a physical connection with a partner. Sometimes you simply have a chemical imbalance, and you need medication. Sometimes you need a change of job, better finances, etc.
Again, loaded question. No, I don't think you can simply choose to be happy, but you can make yourself happy with some work.