How to implement RingtonePreference in PreferenceFragmentCompat?

For today ringtone preference does not exist in the support library. You need to use the framework's version or create your own.
I think it will appear soon

Not my solution, but I post it anyway, because it works.

In you preferences XML resource, change RingtonePreference to Preference. Then, in your implementation of PreferenceFragment, add:

@Override
public boolean onPreferenceTreeClick(Preference preference) {
    if (preference.getKey().equals(KEY_RINGTONE_PREFERENCE)) {
        Intent intent = new Intent(RingtoneManager.ACTION_RINGTONE_PICKER);
        intent.putExtra(RingtoneManager.EXTRA_RINGTONE_TYPE, RingtoneManager.TYPE_NOTIFICATION);
        intent.putExtra(RingtoneManager.EXTRA_RINGTONE_SHOW_DEFAULT, true);
        intent.putExtra(RingtoneManager.EXTRA_RINGTONE_SHOW_SILENT, true);
        intent.putExtra(RingtoneManager.EXTRA_RINGTONE_DEFAULT_URI, Settings.System.DEFAULT_NOTIFICATION_URI);

        String existingValue = getRingtonePreferenceValue(); // TODO
        if (existingValue != null) {
            if (existingValue.length() == 0) {
              // Select "Silent"
                intent.putExtra(RingtoneManager.EXTRA_RINGTONE_EXISTING_URI, (Uri) null);
            } else {
                intent.putExtra(RingtoneManager.EXTRA_RINGTONE_EXISTING_URI, Uri.parse(existingValue));
            }
        } else {
          // No ringtone has been selected, set to the default
            intent.putExtra(RingtoneManager.EXTRA_RINGTONE_EXISTING_URI, Settings.System.DEFAULT_NOTIFICATION_URI);
        }

        startActivityForResult(intent, REQUEST_CODE_ALERT_RINGTONE);
        return true;
    } else {
        return super.onPreferenceTreeClick(preference);
    }
}

@Override
public void onActivityResult(int requestCode, int resultCode, Intent data) {
    if (requestCode == REQUEST_CODE_ALERT_RINGTONE && data != null) {
        Uri ringtone = data.getParcelableExtra(RingtoneManager.EXTRA_RINGTONE_PICKED_URI);
        if (ringtone != null) {
          setRingtonPreferenceValue(ringtone.toString()); // TODO
        } else {
          // "Silent" was selected
          setRingtonPreferenceValue(""); // TODO
        }
    } else {
        super.onActivityResult(requestCode, resultCode, data);
    }
}

Source.