As with some of his other epistles, Paul told the Colossians, in Col 1:9-12, what he had been praying for them.  See Eph 1:16-19, for example.  Paul’s prayer for the Colossians was that they might:

Be filled with the knowledge of his will – Col 1:9 – several verses in the Bible plainly state the will of God: in everything give thanks, 1 Thes 5:18; serve others as you serve Jesus Christ, Eph 6:5-8; abstain from fornication, 1 Thes 4:3-7; submit to the ordinances of men, 1 Pet 2:13-15; be transformed by the renewing of your mind, Rom 12:2; remember that the Lord is not willing that any should perish, 2 Pet 3:9.  God wills additional things, as well.  And Paul prayed that the Colossians would be filled with the knowledge of his will. 

• In all wisdom – it takes wisdom to discern God’s will and to do it.  And this wisdom comes from the Lord, Prov 2:6-7, when you fear him.
• In spiritual understanding – spiritual understanding comes from the inspiration of the words of God, Job 32:8; 2 Tim 3:16-17, and from departing from evil, Job 28:28.

Walk worthy of the Lord unto all pleasing – Col 1:10 – In 1 Thes 2:12, God has called us to his kingdom and glory, so we need to walk worthy of him.  In 1 Thes 4:1, our walk should please God.  He’ll be pleased if we walk by faith, Heb 11:6.

• Being fruitful in every good work – Titus 3:8 – we are to maintain good works; they will be fruitful if they are done to the glory of God.
• Increasing in the knowledge of God – In Phil 3:10 this is something even Paul wanted

Be strengthened with all might, according to his glorious power – Col 1:11 – In Eph 3:16, this strength comes from the Spirit of God in the inner man.  We need the Lord’s strength, not ours, Eph 6:10, Phil 4:13.

• Unto all patience – we must have patience, Jas 1:3-4, for God to accomplish through us what he intends to do.  The process of maturity is slow.
• Unto long-suffering with joyfulness – in the process of your perfection you are going to suffer, 1 Pet 5:10, and the Lord wants you to be able to suffer long (as long as it takes) and joyfully, 1 Pet 4:12-14.

Give thanks unto the Father – Col 1:12-14 – we are to be thankful always for all things, Eph 5:20.  We are thankful to God:

• Which hath made us meet to be partakers of the inheritance of the saints in light. This is a spiritual inheritance that all saints get in light, Eph 1:11, Acts 26:18.
• Who hath delivered us from the power of darkness.  The power of darkness are rulers, Eph 6:12, directly opposed to the Lord, Lk 22:53.
• Who hath translated us into the kingdom of his dear Son.  To translate is to change us from one location to another.  We were translated from the world, under the domination of the devil, 2 Cor 4:4; Acts 26:18, to the kingdom of Jesus Christ.  We are now seated in him in heavenly places, Eph 2:6.

We are thankful to Jesus:

• In whom we have redemption through his blood – we have been redeemed from death.  All the effects of death resulting from the sin of man have been or will be completely abolished.  Our bodies, souls, and spirits will live for ever in eternity.  All of this is through the blood of Jesus, Eph 1:7.  If you have a Bible that removes “through his blood” from Col 1:14, you have a corrupted Bible.
• In whom we have the forgiveness of sins – we have the forgiveness of sins, right now, through the propitiation of Christ for our sins, 1 Jn 2:2.  Yet, sin still affects our fellowship with God.  So, we confess our sins, 1 Jn 1:9, and we are sure that we are forgiven and cleansed by Christ’s shed blood, 1 Jn 1:7.

Conclusion:  Paul’s prayer for the Colossians would be a good prayer for us to pray for our new converts.