Second Peter 3:9 shows us God's heart for those who do not yet know Him: "The Lord is not slow to fulfill his promise as some count slowness, but is patient toward you, not wishing that any should perish, but that all should reach repentance." In John 17, Jesus prayed for eternal life for those whom God gave Him. He also said, "And this is eternal life, that they know you, the only true God, and Jesus Christ whom you have sent" (John 17:3). Clearly God wants people to know Him, and the only way to know God is through Jesus (John 3:15–18; 14:6; Acts 4:12). So it is in line with His will to pray for repentance unto salvation for those who are unbelievers.
What are good prayers to pray for unbelievers?
We can also pray to be used by God to speak the truth to those who may not know it and to tangibly demonstrate God's love to them (Galatians 6:10; Colossians 4:5; Ephesians 5:15–16). Ask for boldness to talk about God (Acts 4:13, 29; Ephesians 6:19). Ask God to enable you to show love to all people (1 John 4:7). Ask Him for wisdom in how to best interact with others both in deeds and in words (James 1:5; 1 Peter 3:15–17).
Ask God to arrange things in such a way that unbelievers turn toward Him. This might include protection and blessing. But often coming to Christ requires that our idols, such as comfort or success or wealth, fail us (for example, see Psalm 119:67). Pray that God will soften the hearts of unbelievers and draw them to Himself (John 6:44), whatever that takes.
Know that even when you don't know how to pray, you can start there, ask God to show you how to pray, and trust that He is taking care of it (Romans 8:26).
Should we pray for the unsaved? Is there biblical basis for praying for the unsaved?
Intercessory prayer – What is it?
What is the importance of praying for others?
Does God hear the prayer of an unbeliever?
Does God hear my prayers?
Truth about Prayer