When I was in college an English teacher made an interesting statement. She said, "Maybe instead of asking if happiness is possible, we should ask ourselves if it is even desireable. Should even be set as a goal?" I found that thought provoking.
There is a school of thought that believes human learning and advancement only comes from confronting and overcoming problems. That is how we grow and change. Remove the problems (challenges) and we stagnate. Is happiness the equivilent of stagnation? Is happiness the same as complacency or contentedness? People become activists because they are not happy with the current situation.
I personally think that happiness is not an end to seek, but a by product of how you live your life. If, at the end of the day, you like the person in the mirror, you will be a reasonably happy person.
Of course, if one is clinically depressed, it becomes more complicated.