The Bible doesn't teach a specific age of accountability as in a numerical year, but rather as being able to understand. I believe the best passage that deals with an age of accountability is Romans 7:7-11:
7What shall we say then? Is the Law sin? May it never be! On the contrary, I would not have come to know sin except through the Law; for I would not have known about coveting if the Law had not said, "YOU SHALL NOT COVET." 8But sin, taking opportunity through the commandment, produced in me coveting of every kind; for apart from the Law sin is dead. 9I was once alive apart from the Law; but when the commandment came, sin became alive and I died; 10and this commandment, which was to result in life, proved to result in death for me; 11for sin, taking an opportunity through the commandment, deceived me and through it killed me.
Paul states here that he was alive apart from the Law. But once he learned the Law and had understanding of what God's standard was in regards to coveting, he became a covetous person and then (spiritual) death came. This would be the so called "age of accountability", this time when a child who was innocent because of ignorance of the Law, gains a fuller understanding of God's Law and then deliberately chooses to ignore the Law and enter into sinful desires and actions.
In Paul's case, because he was raised a Jew, he probably learned the Law at an earlier age. Earlier, in Romans 1, Paul talks about those who come to know God, not through the Law, but through His invisible attributes in creation. Again, the language that Paul uses is "For even though they knew God, they did not honor Him...". In this passage Paul is speaking not only of Jews, but of "the Greek" which can be translated everyone who wasn't a Jew. And Paul speaks of everyone having "known" God, but then having rebelled against Him and God then gave them over to their passions.
All children, no matter from what nation or tribe, start off having that full child-like faith in God. (I know, atheists are bound to disagree with me on this, but I'll stand by my assertion here.) Then as time goes by, the rebellious nature begins to take over. Children of those who know and love God will still rebel, especially once God's holy standards are taught to them, but nonetheless have the advantage of knowing those standards and knowing their need for God at a much earlier age. Sin will come, but the solution to sin also comes. Children who will never hear of God in their lives, will still carry with them that lifelong conviction that there is a morality which, even if they don't understand its source, is something that they must live up to. They won't and will be just as subject to God's judgments as those who do know God.
At what age does a child step from innocence into rebellion? No set time, just when they can gain an understanding of the difference between what they should do and why and then deliberately choose not to.
