I agree with Marks definition of happiness, and would suggest that joy is the more transient experience, though no less real.
There used to be an in-house christian joke in the UK about people who claimed to have the "joy of the Lord" but seemed on the surface quite miserable. It was something along the lines of "his/her joy is so deep it's invisible". I know people like that, and it is kind of sad. They will say that there is a spiritual christian joy which is beyond the comprehension of other mortals whilst finding it impossible to see anything good about the world we live in.
Personally I believe that joy exists and that everybody can experience it regardless of religious or non-religious beliefs. Joy I would define as an ecstatic sense of aliveness that, as implied in CS Lewis's book title "Surprised By Joy" can emerge out of nowhere when we are in the habit of looking in anticipation at the world around us. I've not had that sense very often at all, and never, unlike CS Lewis, when I was a christian.