The most important thing you can do is to pray for your friend. You can't change his heart and mind; even if you answered every argument he threw at you, he'd probably still keep clinging to his unbelief.
But God can break through his resistance and open his eyes to the truth -- and that's one reason why prayer is so important. In other words, God can do what we can't do -- and He often does, as we pray for those who don't know Christ and may not want anything to do with Him. The Holy Spirit is far greater than we are, and He is able to break through even the hardest heart. The Bible says that "When he comes, he will convict the world of guilt in regard to sin and righteousness and judgment" (John 16:8).
The other thing you can do, however, is to be an example to your friend of Christ's love and transforming power -- both by your words and your life. Even the strongest argument can't stand up to the reality of a changed life. The Bible says, "Be wise in the way you act toward outsiders; make the most of every opportunity" (Colossians 4:5).
I suspect that down inside your friend is unsure of his convictions; otherwise why would he feel compelled to argue so much? Don't be discouraged, and don't give up on him. Some of God's greatest servants over the centuries were once atheists.