Happiness vs God

Is knowing God and being happy an either/or choice? Does choosing one automatically exclude the other? When pastors (me included) say God is interested in your holiness, not your happiness, the wall between the two feels pretty thick. Yet what does the Bible actually say about God and happiness? Is it possible God Himself has the capacity for infinite happiness? What would that mean for me, if true? What would I lose if it was true and I missed it?