This is an interesting topic for a speech or an essay; however, it rests on the premise that the only way to be happy is to believe in God. While you and I might agree on that premise, there are certainly millions of people in the world who would not. I assume you are writing some version of a personal essay in which you take a position you believe to be true and then defend it. If that is the case, perhaps you would be better served to make this your premise: In my experience, true happiness can only be found through belief in God. For now, however, I will assume your premise is true and offer a few points of support for it.
First, believing in someone higher (and better and more powerful) than oneself is reassuring. This is a common factor in almost every religion and faith. In a world where awful things happen every day, it is a comfort to know that Someone is in control. While bad and evil things still happen as a result of sin in our world, God still has ultimate control of His creation.
Second, belief in God brings comfort in difficult times. We can talk to him through prayer and find solace in His Word.
Third, in addition to hope and comfort here on earth, God has promised eternal life in Heaven to those who believe.
Again I remind you that your premise may be flawed; I will also remind you that happiness is not something God promises. Christians, like everyone else, must choose to be happy. (You know this is true if you have met many people who call themselves Christians; not all of them are happy.) Psalm 68:3 says:
But may the righteous be glad and rejoice before God; may they be happy and joyful.
Happiness is a choice, not a gift provided from God--though certainly He gives believers a reason to be happy. (This principle is true in the secular world, as well; note that the Constitution only gives Americans the right to pursue happiness by providing the freedoms for people to do so; happiness cannot be mandated.) Happy writing!