Can someone be genuinely converted and contentedly live in sin?

Generally speaking, no.

• John is absolutely clear: only those who walk in the light, obey God’s commandments, and love other Christians are genuinely converted (1 John 1:6-7, 2:4-6, 3:7-8).
• Paul makes the same point when he writes, “Do you not know that the unrighteous will not inherit the kingdom of God?” (1 Cor. 6:9). Elsewhere he says plainly, “If you live according to the flesh, you will die, but if by the Spirit you put to death the deeds of the body, you will live” (Rom. 8:13). Those who actively fight against sin and pursue righteousness are genuine Christians.
• Jesus himself says, “A good tree cannot bear bad fruit, and a bad tree cannot bear good fruit. Every tree that does not bear good fruit is cut down and thrown into the fire” (Matt. 7:18-19, NIV). Everyone who has been born again bears good spiritual fruit, marking him or her off from the world (see also Matt. 5:13-16, Matt. 7:21-22).

While no Christian is perfect in this life, the New Testament insists that only people whose lives demonstrate genuine spiritual fruit have been born again.