Here is the Apostle Paul praying for King Agrippa and other unbelievers who were listening to him, that they would become a Christian like him...Acts 26:29 "...I pray God that not only you but all who are listening to me today may become what I am, except for these chains." 

Here Jesus commands us to pray for our persecutors (unbelievers) and it is implied that we pray for their greatest need: salvation...

"Love your enemies and pray for those who persecute you..."  [Matthew 5:44]

"...bless those who curse you, pray for those who mistreat you.  [Luke 6:28]