A clear invitation to pray
Paul urged Timothy's church to make prayers, requests, intercessions, and thanksgivings for all people. He connects this broad prayer with God's saving purpose. That includes neighbours, relatives, leaders, friends who are indifferent to faith, and even people whose choices trouble us (1 Timothy 2:1-4).
So praying for an unbelieving person is not a lesser kind of prayer or a vague hopeful gesture. It fits God's own heart. You can bring a specific name before God and ask him to show that person the truth and kindness of Jesus.
I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men; For kings, and for all that are in authority; that we may lead a quiet and peaceable life in all godliness and honesty. For this is good and acceptable in the sight of God our Saviour; Who will have all men to be saved, and to come unto the knowledge of the truth.
Paul prayed for his own people
Paul knew that many of his fellow Israelites did not recognise Jesus as the promised Messiah. He did not respond with superiority or give up on them. He told the Roman Christians that his heart's desire and prayer to God for Israel was that they might be saved (Romans 10:1).
That is a helpful pattern when someone you love does not share your faith. Honest grief can become prayer. Rather than trying to win every argument, you can ask God to meet them, open a door for a good conversation, and give you patience and love.
Jesus prayed for those opposing him
At the crucifixion, Jesus prayed for the people involved in his death, asking the Father to forgive them because they did not understand what they were doing (Luke 23:34). His prayer shows remarkable mercy towards people who were far from him.
This does not mean pretending sin is harmless. Jesus came precisely because sin is serious. But it does mean Christians can pray for people who are hostile, dismissive, or wounded, trusting God to bring conviction, forgiveness, and new life.
Then said Jesus, Father, forgive them; for they know not what they do. And they parted his raiment, and cast lots.
Prayer is not control
The Bible holds together God's powerful work and a real human response. Jesus said that no one comes to him unless the Father draws them (John 6:44). That gives real hope in prayer, because no heart is beyond God's reach.
Yet prayer is not a way to make God override someone or guarantee a timetable. Keep praying, keep loving, and speak about Christ with gentleness when the opportunity is right. You might pray simply: 'God, please draw them to Jesus, help them see what is true, and show me how to love them well.'