What is it you want them convicted of?
The Holy Spirit will convict a person of their need for a saviour. Our own mind and heart will convict us of sin. Because of Jesus, sin is no longer a problem between God and us. Sin is a problem in our lives because it is a habit. When we are saved we are no longer "sinners". A sinner is someone who is not saved, by Biblical definition. After being saved we sin from habit and we need our minds renewed to the Word of God. Sin in our lives will keep us from realizing the blessings God has already given us. We no longer have to "work" in order to have God give us blessings, but we do have to apply ourselves to "fit into" the blessings He has given us.
The goodness of God draws people to repentance. Judgment does not draw people to salvation. Praying for your enemies and doing good to our enemies is what Jesus has done, and is doing through believers. Believers are supposed to demonstrate the goodness of God.
In the name of Jesus, I bless your enemies with the life and goodness of God.