In order to track who should play next, we need to store who played last:

private char lastPlayer = '';

public void play(int x, int y) {
  checkAxis(x);
  checkAxis(y);
  setBox(x, y);
  lastPlayer = nextPlayer();
}

public char nextPlayer() {
  if (lastPlayer == 'X') {
    return 'O';
  }
  return 'X';
}

You are probably starting to get the hang of it. Tests are small and easy to write. With enough experience, it should take a minute, if not seconds, to write a test and as much time or less to write the implementation.