I don't know if there are more atheists than there used to be, although it's possible, since there are more people in the world. But it does seem they are more vocal, and because our society is getting more secular their message often gets more of a hearing.
An atheist is a person who believes that God doesn't exist (in contrast to an agnostic, who says he doesn't know whether or not God exists). But look carefully at that definition: An atheist believes God doesn't exist. He can't prove it; he can't verify it; he can't demonstrate it. He lives only by faith -- faith that he is right, and everyone else is wrong.
Often, however, people who claim to be atheists don't reject God because they've examined all the evidence and concluded there is no God. Instead, they reject God for one reason: They don't want anyone (including God) to interfere with their way of living. Not all atheists are bad or immoral; some live commendable lives. But it's also no accident that some of the worst atrocities in human history were committed by regimes that were based on atheism. No wonder the Bible says, "The fool says in his heart, 'There is no God.' They are corrupt, and their ways are vile" (Psalm 53:1).
Pray for your cousin; only God can convict him of his sin and open his eyes to the truth of Christ. Also, pray that you will be an example to him of Christ's love and compassion, even if others in your family reject him.