I thought it was a great question, and here is my rather long-winded attempt to answer it.
Happiness vs Joy
Joy is a word frequently used in the Bible to denote happiness and gladness. However, it is important to make a distinction between joy in the Biblical sense (I will call it biblical joy) and an emotional happiness.
Biblical joy is not just an emotional state, but a quality or a characteristic of the believer. The believer has joy at all times, in all circumstances, even in the face of great trials. (See Phil 4:4). The object of Christian joy is in the person of Christ Himself: whether our surroundings are good or bad, we recognise that He himself is sufficient for our needs, and we will never lose His love or faithfulness. Biblical joy is not something that we conjure up ourselves, through self-affirmation or pep talks - it is given by God (Rom 15:13), and is one of the fruits of the Holy Spirit.
Happiness is different. It is an emotion, not a character. Many things make us happy, usually for perfectly legitimate reasons. Roast on a winter's night, cold beer in a summer's eve, a lover's embrace, a baby's chuckle, the list goes on. A person (Christian or non-Christian) may very well live generally contented lives: enjoying prosperity, the love of their family and friends, content in their jobs and hobbies.
It is, I believe, imperative to make a distinction between Biblical joy and happiness. Without such a distinction, you may expect Christians to be happy all the time, and non-Christians to be always miserable - and this is simply not the case.
Some facts about joy:
1. Christian joy is joy in the Lord. (See Phil 4:4)
Christian joy flows from a relationship with Christ. We don't rejoice because Christ has given us a nice job, nice family, or a healthy body. We don't even rejoice even because Christ has saved us from hell. Christian joy is simply joy in the Lord - a simple recognition that Christ is all things great and glorious, Christ is great strength and great beauty all in one, and simply that we get to have a relationship with Him. We rejoice over the good news - the wonderful news - that for this relationship to be made possible great sacrifice had to be made, and He has made it. Thus, we rejoice over who He is, what He has done, and our bond with Him.
2. Christian joy is a fruit of the Spirit (Galatians 5:22-23)
When we have a relationship with Christ, we are given the gift of the Holy Spirit. The Spirit works in our lives in such a way that it gives visible results - or, to use the language of Galatians, bears fruit. It is important to note that these are not our fruit, but the Spirit's. Therefore, Christian joy can not be "produced" by some self-affirmation pep talk, nor by some self-applied cognitive behavioural therapy. You can not make a New Year's resolution to have more joy - it simply will not work. Instead, we take our eyes off ourselves, on to Christ, and joy naturally flowers and fruits.
3. Joy in all circumstances (Phil 4:12, James 1:2-4)
In Phil 4:12, Paul informs us that he has learned the "secret" of facing all situations, whether good or bad. Earlier in the same chapter, he gives us the key to the secret: we are to rejoice in the Lord, because He is at hand and He gives us peace. If we are to rejoice in the Lord, then we will indeed have surpassing joy - because Christ surpasses everything! In a world of uncertainty and change, Christ's nature doesn't change, the work of Christ on the cross doesn't change, and our relationship to Him doesn't change. What is most of value to us - above health and wealth - Christ Himself - will not be taken from us, although our health may fail and money flows in and out of our bank accounts almost as if it has a life of its own.
James gives us another reason to have joy in tough circumstances: because they produce steadfastness (James 1:2), or endurance in our faith. Our trials and sufferings produce a deeper, more steadfast faith in Christ, enriching and deepening our relationship with Him - and in this we rejoice! So, even in our trials, the source of our joy and the focus of our attention is still Christ.
OK... so how does this apply to me?
1. Does this mean that Christians should be happy at all times?
3 years ago, my father-in-law passed away after a swift battle with cancer. Our family was devastated - but particularly my mother-in-law. They had been happily married for over 30 years, lived through some terrible trials together, and was just starting to enjoy a more stable lifestyle. She was shattered. During those days, if somebody had come up to her and said, "Why are you sad? Christians should always be happy!", I might very well have punched them in the face.
The Bible does not teach that Christians should be stoical in all situations. Jesus was not a stoic - he wept, anguished, got angry, and sweated blood. In the passages of the Bible where it talks about rejoicing in all circumstances, there is a recognition that these circumstances causes grief and suffering. (See Romans 5:3-4, 1 Peter 1:6-7.) These books, often written during times where Christians faced terrible persecution, showed a raw and acute awareness of the devastation life can throw at us. However, these passages does give us encouragement and point us toward the object and source of our joy, Christ Himself. My mother-in-law is not perfect (which daughter-in-law will admit that?), but I do know that her ultimate comfort, and joy, came from Christ.
2. So, what should we say to non-Christians who seem to have it all?
A couple of years ago, my brother-in-law started doing some work placements inside a hospital, where he met many doctors. He was amazed - these doctors were smart, altruistic, compassionate, hard working, secure, and friendly. And none of them were believers. "They are happier than you are," he said to me, somewhat accusational in his tone, "and they laugh at Christians."
C. S. Lewis, in his book The Pilgrim's Regress, suggest that we are all searching and yearning for a place of absolute beauty, where all of our desires and needs are ultimately fulfilled. Various things in life give us an "image" of what that place is like - poetry, music, entertainment, food, and even love from our family and friends - all give us a faint taste, a little snippet, of that place of ultimate fulfilment. But these things are only good as sign-posts: when you pursue them for their own sake, the faint happiness you get from them disappears like a mirage, leaving behind only despair and addiction. (Think about the hypochondriacs who obsess about their health so much they lose their enjoyment of their health; the foodie who descends into bulimia; the doting mother whose happiness is so entangled in her son that both of their lives are a misery.) A non-Christian do not always have to fall into the extremes of addiction and despair - you can ostensibly enjoy a little bit of everything without being completely addicted to it. And certainly - the happiness that you get out of a hot roast or a cold beer, or your wife's embrace - is all very, very real.
But I would tell my non-Christian friends who live happy lives - that their happiness is but merely happiness, which is only a shadow or a mirage compared to the deeper, eternal joy that they could have in Christ. Examine each source of happiness, examine it closely and you'll see smoke and mirage. The fulfilment that we have in Christ - is so much bigger, more joyful, more fulfilling, more solid - and so much more freeing than any other happiness that we can have. We know, deep down, that this kind of fulfilment is impossible for us who are mere human - and yet Christ has made it possible. And that is the good news.
