在Android TV（Leanback）应用程序中，可以使用片段（Fragment）和自定义对话框来创建类似于AlertDialog的权限对话框。以下是一个解决方法的示例代码：

1. 创建一个自定义对话框类（CustomDialogFragment）来显示权限对话框：

public class CustomDialogFragment extends DialogFragment {
    private static final String ARG_TITLE = "title";
    private static final String ARG_MESSAGE = "message";
    private static final String ARG_POSITIVE_BUTTON = "positive_button";
    private static final String ARG_NEGATIVE_BUTTON = "negative_button";
    private static final String ARG_PERMISSION = "permission";

    private String title;
    private String message;
    private String positiveButton;
    private String negativeButton;
    private String permission;

    public static CustomDialogFragment newInstance(String title, String message, String positiveButton,
                                                   String negativeButton, String permission) {
        CustomDialogFragment fragment = new CustomDialogFragment();
        Bundle args = new Bundle();
        args.putString(ARG_TITLE, title);
        args.putString(ARG_MESSAGE, message);
        args.putString(ARG_POSITIVE_BUTTON, positiveButton);
        args.putString(ARG_NEGATIVE_BUTTON, negativeButton);
        args.putString(ARG_PERMISSION, permission);
        fragment.setArguments(args);
        return fragment;
    }

    @NonNull
    @Override
    public Dialog onCreateDialog(Bundle savedInstanceState) {
        title = getArguments().getString(ARG_TITLE);
        message = getArguments().getString(ARG_MESSAGE);
        positiveButton = getArguments().getString(ARG_POSITIVE_BUTTON);
        negativeButton = getArguments().getString(ARG_NEGATIVE_BUTTON);
        permission = getArguments().getString(ARG_PERMISSION);

        AlertDialog.Builder builder = new AlertDialog.Builder(getActivity());
        builder.setTitle(title)
                .setMessage(message)
                .setPositiveButton(positiveButton, new DialogInterface.OnClickListener() {
                    public void onClick(DialogInterface dialog, int id) {
                        // 请求权限
                        requestPermission(permission);
                    }
                })
                .setNegativeButton(negativeButton, new DialogInterface.OnClickListener() {
                    public void onClick(DialogInterface dialog, int id) {
                        // 用户拒绝权限，关闭对话框
                        dialog.dismiss();
                    }
                });
        return builder.create();
    }

    private void requestPermission(String permission) {
        // 请求权限的代码
    }
}

2. 在活动（Activity）中使用CustomDialogFragment来显示权限对话框：

public class MainActivity extends FragmentActivity {
    private static final String TAG_DIALOG = "dialog";

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        // 检查是否有权限
        if (!hasPermission()) {
            // 显示权限对话框
            showPermissionDialog();
        }
    }

    private boolean hasPermission() {
        // 检查权限的代码
        return false;
    }

    private void showPermissionDialog() {
        CustomDialogFragment dialog = CustomDialogFragment.newInstance(
                "权限请求",
                "需要获取您的位置信息以提供更好的服务，是否允许？",
                "允许",
                "拒绝",
                Manifest.permission.ACCESS_FINE_LOCATION);

        FragmentManager fragmentManager = getSupportFragmentManager();
        dialog.show(fragmentManager, TAG_DIALOG);
    }
}

上述代码中，CustomDialogFragment类继承自DialogFragment，用于创建自定义对话框。在onCreateDialog()方法中，使用AlertDialog.Builder来创建对话框，并设置标题、消息和按钮的点击事件。通过newInstance()方法传递参数给CustomDialogFragment类。在活动中，通过showPermissionDialog()方法来显示权限对话框。

注意：在真实的应用程序中，需要根据实际的权限需求和逻辑进行相应的修改。