Masters, treat your slaves justly and fairly, knowing that you also have a Master in heaven.
You might read this verse and ask, why Paul didn't say, "free your slaves right now, if you want to be a Christ follower". That's my first reaction. But he didn't say that. This is God inspired scripture.
In the New Covenant, God changes people from the inside out. The whole law is valid, but now God changes people from the inside. Slave owners, in a slave culture, were joining the church in droves. People "came as they were" when Christ called them and their transformation began. It doesn't take long for a slave owner to see that God is calling slaves to Christ and we are all the same. In Christian community, the slave owner is going to be changed and eventually free his slaves or let them stay on as real workers, but it starts with treating them justly and fairly. We know that slavery is not just or fair. Treating slaves justly will ultimately result in the slaves freedom, because that is the ultimate justice. If you look elsewhere in Paul, you see this (1 Cor. 7., 1 Tim. 6, Acts 17). See Albert Barnes Colossians Commentary for good notes on this here. Within 200 years, the Roman Empire no longer had slavery.
You could make the argument that things did not go right when Christians in America realized how evil slavery was. Half of the states did not agree and decided to go to war and die and kill those trying to impose their law on them. Could the civil war have been avoided if the church had instead kept being transformed from within finally working Christ into the hearts of the majority of slave owners, thereby transforming society? I think so and that is still God's way. The people in the church today need radical transformation and then need to go into society and transform it, rather than an untransformed church imposing Christian law on a rebellious society, causing a culture war.