I think that if you tried to maintain a state of constant joyfulness, you would be doing yourself some damage! Joy is usually a reaction to an event or occurence, and probably involves increased heart rate and a surge of adrenalin (I'm no expert, I'm just going on what joy means to me).
Happiness is a state that can be maintained very easily, and would be preferable to a state of constant joy (to me) because it can be calm, it can be all-pervading and is easily recognisable. If I lose sight of my happiness I am familiar enough with it to be able to locate it again very quickly. I can't locate joy in the same way.
Joy is something that I experience unexpectedly. Happiness is something that I experience daily through choice - I choose to be happy, but other people tend to be the one's who bring me joy.