Can atheists be happy? Sure they can. But their criteria for obtaining happiness is radically different from a Christian's because their objectives are so different that they can't even understand Christian happiness.
To an atheist happiness is purchased by success. There is no god, there is no higher meaning for our lives, so the only thing we can really gain is being successful. And without a god, success becomes measured by how good we are at this life thing.
Life can be compared to a video game. There are tools you need to use to get through it, there is a story to follow and there are objectives to be met. For an atheist, success is measured in how good you are at playing the game. If you are good at gathering money, influencing other people, gaining power and extending your life span, you are successful at this game. Winning is counted by how long you live, how many things you have enjoyed and how much you have.
Christians aren't so focused on tools and resources. They are more interested in the game's story. We know the tools are important, but we don't put mastering the game mechanics above the storyline. Our profit is in living our lives well, not just mastering the game. Money and even longevity don't matter as much to us. (This is why Peter and Paul, both already aware of how they would die, could still have joy. Living a long time is not success to a Christian.)
This is also why atheists think Christians are stupid. The things that they think are all-important for being successful at life are things we don't really care much about. But if you accept the initial premise that there is no god, no life after this one, then their values are actually logical. If this were the only life you had, it really would be stupid to not get all the resources you can grab.