I'll propose a definition so that others may refine and build of off it (or reject and counter it):
The science of happiness is the systematic organization of knowledge (e.g. testable theories, empirical results, and predictions) about the way human beings
- and most importantly, are affected by
goals—a "goal" being: a mental picture of a desired future.
I am by no means attached to the definition of "goal," nor even the word "goal" (as opposed to "desire", "aim", etc.), nor the 4-way breakdown. I do however contend that the definition of a "goal" should be rooted in psychology or cognitive science. And to explain the 4-way breakdown:
By formulation, I mean the way we consciously and subsconsciously generate goals: whether they be short-term or long-term, realistic or idealistic, constructive or destructive.
By pursuit, I mean the way we connect the dots from our present state, however we perceive it, to our future state, however we imagine it, i.e. again, our goals.
By achievement, I mean the way we employ techniques that create real (non-deluded) progress toward our goals.
By affection (or effects, for the less linguistically-flexible), I mean the way we are affected, negatively or positively, by the way we formulate, pursue, and achieve our goals: whether they be depression or mania, lacking or excessive confidence, procrastination or proactivity.
Indeed, this last item, the effect of our formulation, pursuit, and achievement of goals, may be a better and more focused choice—perhaps to define all of "the science of happiness" by—since the other items may compete with SE sites on psychology, cognitive sciences, personal productivity, physical fitness, etc.