Happiness is only measurable in relation to sadness. If you were "happy" all the time you wouldn't feel like you were happy because that would be your default state - you would just feel normal.

>One could aim for "contentment". Even that is unattainable for most people.

That has been my goal, which has been more or less achieved. What more can you really ask for or expect out of life? Sometimes extraordinarily bad things are going to happen, and you are going to feel sad for a while. Likewise, sometimes extraordinarily good things happen, and you are going to feel happy for a while. But you can't (shouldn't) live your life with the ever-present anticipation (or dread) of these infrequent events. We're all on this planet for a very short time in the big scheme of things, and we'll all experience a variety of pleasant and unpleasant things. At the end of the day all you can do is navigate down the bumpy road as best you are able and not worry about things that are outside your control.