The most important thing you can do is to pray for your neighbor. That may not seem like much, but he needs God's help right now (whether he realizes it or not), and one of the ways God uses us to help others is to pray for them.
In addition, be a friend to him. I don't know his whole story, of course, but often divorce is just as shattering as the death of a loved one. Like death, it marks a final separation, and like death, it brings with it loneliness and even guilt over the past. He's facing one of the hardest situations any person will ever face, and he needs the friendship of others. The Bible says, "Carry each other's burdens, and in this way you will fulfill the law of Christ" (Galatians 6:2).
In addition, don't hesitate to invite him to your church. If he accepts, pray that God will touch his heart and draw him to Christ. After all, the most important decision any person will ever make is the decision to follow Jesus. He may be open to God in a way he never has been before.
But even if he refuses, keep on being his friend. Christ doesn't stop loving us if we first refuse Him–and neither should we with other people. The Bible says, "Love your neighbor as yourself" (Mark 12:31).