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. 

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.

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.

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:

We are thankful to Jesus:

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