I am quick to pray for the unsaved because I was unsaved at one point...we all were.
But remember that once you witness, your job is done. All you can do is make sure there's no sin or hypocrisy in your life that the unsaved sees...that causes the unsaved to blaspheme. How many people don't become Christians because of the Christians' behavior! Doesn't excuse them, but Christians often hinder the unsaved from coming to Jesus.
Once you have made sure there was no sin in your life, all you can do is pray. No one comes to God unless the Father draws them. Pray the Father draws them.
Your friend'x uncle is in my prayers, and I was praying for him to come out of the ICU. That was answered. Maybe the prayer for his soul will be answered too.