Prayer is important but it is not a substitute for the Gospel.

Matthew 9:38, "Pray ye therefore the Lord of the harvest, that he will send forth laborers into his harvest."

MATTHEW 9:35-38, 13:53-58, MARK 6:1-6 (NKJV)

Jesus Rejected at Nazareth

6 Then He went out from there and came to His own country, and His disciples followed Him. ² And when the Sabbath had come, He began to teach in the synagogue. And many hearing Him were astonished, saying, “Where did this Man get these things? 

And what wisdom is this which is given to Him, that such mighty works are performed by His hands! ³ Is this not the carpenter, the Son of Mary, and brother of James, Joses, Judas, and Simon? 

And are not His sisters here with us?”

 So they were offended at Him.

⁴ But Jesus said to them, “A prophet is not without honor except in his own country, among his own relatives, and in his own house.” ⁵ Now He could do no mighty work there, except that He laid His hands on a few sick people and healed them. 
  ⁶ And He marveled because of their unbelief. Then He went about the villages in a circuit, teaching.

People are born again through the power of the Word of God, not through prayer.
 Prayer is very important, but it is not a substitute for the Gospel.

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Many people petition God for someone to be saved and can't understand why it hasn't happened yet.
 We don't have to ask the Lord to save anyone.
 He isn't willing that anyone should perish.
 He has already made provision for everyone's salvation.

So what do we pray concerning someone coming to the Lord?
 Jesus said to pray that the Lord send laborers across their path. 
They need to hear the Word. Also, we should bind the influence of the god of this world (Satan) who tries to blind them to spiritual truth 

2 Corinthians 4:4 New King James Version (NKJV)

⁴ whose minds the god of this age (Satan) has blinded, who do not believe, lest the light of the gospel of the glory of Christ, who is the image of God, should shine on them.

  God is more motivated to save our loved ones than we are. 
We don't need to plead with Him, but rather we need to become a channel for Him to flow through to reach that person. 
We do that by sharing the good news (Gospel) with them and/or praying that others will come across their path who will do the same.

The Gospel is the power of God that releases the effects of salvation in our lives. 
Romans 1:1-7  (NKJV)

Greeting

1 Paul, a bondservant of Jesus Christ, called to be an apostle, separated to the gospel of God ² which He promised before through His prophets in the Holy Scriptures, ³ concerning His Son Jesus Christ our Lord, who was born of the seed of David according to the flesh, ⁴ and declared to be the Son of God with power according to the Spirit of holiness, by the resurrection from the dead. ⁵ Through Him we have received grace and apostleship for obedience to the faith among all nations for His name, ⁶ among whom you also are the called of Jesus Christ;

⁷ To all who are in Rome, beloved of God, called to be saints:
Grace to you and peace from God our Father and the Lord Jesus Christ.

If a person needs healing, it's in the Gospel, it's in the Gospel. 
Prosperity, answered prayer, joy, peace, love - they are all found through understanding and believing the Gospel.

The Gospel is the good news that although we are all sinners and worthy of God's wrath, God, in love, sent His Son to be our substitute, bearing our punishment, so that we could be made completely righteous in His sight. It's based only on our faith in this completed work of Christ and not our own performance. 

Now that's the GOOD NEWS!