There are several types of prayers. For example, the Church (commemoration at the Liturgy in the temple) and privately ( prayers at home). You can also distinguish between prayers for the health and repose, pleading, thanksgiving, and repentance. There is a congregational prayer, when a few people gather to make requests to God, and along with it is private prayer. For all the baptized people of the Church allowed to pray in the temple, and for the rest the person needs to make requests to God at home.
In the Christian tradition it is impossible in the Church to commemorate the unbaptized because these people are not members of the Church. But they can not leave without prayer. Any request for a person you can say at home in front of the icons. There can be used as common prayers from the prayer book (on health, repose or other), and to use his words. The Lord looks not just boilerplate text, but sees in the human heart and soul. Every request for any person must be from the depths of the heart.
For the dead unbaptized people can pray in Church, but you can't order remembrance. Nobody forbids to pray in your own words. This can also be done at home. There are even special canons in the prayer for such cases. Practice of prayer Martyr Uaros about those who received not the sacrament.
You can read the Psalm in memory of the departed and the living. And, of course, if the man himself is a believer, he can ask the Lord not just about helping one's neighbor, but that the Lord granted a native or a familiar person to receive the sacrament of baptism.
In some prayer books contain special petition to unbaptized people. Such prayers a lot, so anyone may wish to turn to God. Just buy in the temple like the book and safely perform the feat of love for others, with their roots in prayer for him.