I am a convert to Orthodoxy and was baptized just two years ago, so I don't know if the prayer that I pray for family and friends is appropriate or not, but I pray the following prayer and then name particular family/friends individually. I hope this may be helpful.
Lord, have mercy and save my family and friends. Give them blessings now and salvation in the life to come. Deliver them from all heresy, enlighten them with the Light of Your Truth and unite them with the Holy Orthodox Church.
Pray for me, a sinner,
Martha