According to the author of the book, Josiah was a very young boy, just eight years old, when he became the king and was in charge for a long time in a city called Jerusalem. His mom's name was Jedidah, and she was from a place called Boscath.
2 Kings 22:1: Josiah [was] eight years old when he began to reign, and he reigned thirty and one years in Jerusalem. And his mother's name [was] Jedidah, the daughter of Adaiah of Boscath.
This verse states that Josiah was eight years old when he began to reign, which agrees with 2 Kings 22:1 and therefore does not provide a contradiction.
2 Chronicles 34:1: Josiah [was] eight years old when he began to reign, and he reigned in Jerusalem one and thirty years.