Here is a prayer I like to pray for the "not yet saved" from Acts 28:25-27:
Dear God, Open their eyes so they can see you; Open their ears so they can hear you; Soften their hearts in understanding, so that they can turn that they be healed.
and if you like add (from 1 Thess. 5:7-8), awaken them from their slumber, so that they are no longer people of the night. Amen.