You can point him in the right direction—but to be honest, you can’t win him over by yourself (as you’ve discovered). He’s convinced that he is right—and even if he has secret doubts, his pride probably gets in the way.
But God can do what we can’t do, and He can conquer even the most stubborn heart. And that’s why the most important thing you can do for your friend is to pray for him, asking God to convict him of his sin and his pride and convince him of his need for Christ. Pray also that your life will be a witness to him—a witness to Christ’s peace and joy. People may argue with what we say—but they can’t argue with the reality of a life that’s been transformed by Christ.
In addition, encourage him to face honestly the consequences of his atheism (which many atheists, I’ve discovered, never do). If God doesn’t exist (as he claims), then he has no hope of life after death. Nor does he have anyone to turn to when he needs guidance, or when life turns against him. He is like those of whom the Bible speaks, “without hope and without God in the world” (Ephesians 2:12).
Most of all, urge him to examine Jesus Christ honestly and openly, as He is found in the Gospels of the New Testament. When he does, he’ll discover not only that God exists, but God loves him and wants to come into his life.