People with strong religious beliefs will always be happier for the simple reason that they think that their existence serves a purpose. Service to a higher power and the pursuit of moral superiority make them happy, albeit a little smug. Hence the expression "Holier than thou." It should be mentioned too, that when life gives these zealots lemons they make lemonade because they will always be loved by their deity and there is a purpose to everything that happen--good or bad. They will be rewarded in the end, so they can keep their chins up.
Religion, or rather a belief in a supreme being, someone who is in charge, tends to give a person a sense of relief. Just as a child needs a parent who will guide him or her along the way of life, so do all people need a guardian to guide them through life. If one knows that there is light at the end of the tunnel, that there is something more, they are not only happier in the present, but will want to lead an exemplary life to ensure they reap the promised rewards in the future.
There is this myth that religious people are more happy than non religious people, this is because religious people often commune with other people who believe the same things that they do, this makes them feel safe and secure. As an atheist I commune with other people for different reasons other than their belief system. This means that I am just as happy as any religious person.
The concept that morals come from religion is utterly ridiculous. Morals existed long before humanity had come up with any kind of mythology. I consider myself to be a very moral and ethical person. I always try to do things that are good, simply because I know how it feels to be in a situation where there is no one to help you.
I personally believe that religious people (Christians in particular) are actually less moral than many atheists. You see Christians believe in a very black and white version of morality, for instance stealing is bad no matter what. But imagine someone was dying from a disease that was very easily cured with a very cheap medicine, but you have no money. You have already tried to raise the money and had even begged at the pharmacist's shop for the medicine but had been refused.
What would you do?
A truly christian approach would be that stealing is wrong under any circumstances, so we shall sit down and pray that they get better.
My morals tells me that a human life is worth so much more than some cheap medicine. So if I was in that situation I would steal the medicine to save the person's life.
Christians would say that this action was immoral because some ancient passage in a book says that stealing is wrong. But I know that there is more to morals than simple black and white right and wrong.
I do not think that happiness can only come from being religious. I have tried a lot of different churches in my years and I don't remember the people being that happy or friendly then or now. You also can't say that religion gives you more morals. I was raised by parents that never went to church. I was still taught right from wrong.
Nor does it count when you are bullied into being moral with the threat of Hell. "Is that which is good commanded by God because it's good, or is it good because God commands it?" Morality based on the absolute say-so of a supreme being seems to be no less arbitrary than the relativistic morality that theists decry. God commands rape and murder several times in the Old Testament. For example, in Numbers 31:1-54 God commands Moses and his army to "Kill every male among the little ones, and kill every woman that hath known man by lying with him. But all the women children, that have not known a man by lying with him, keep alive for yourselves." The army comes back with 32,000 virgins after doing God's will...