Well it is a loaded question.
If you edit the script files you will see a value called
regonly" => 0,
That allows a guest to see the item.
Changing the value to
regonly" => 1,
Requires the item to be visible only to registered visitors.
At this point I am not sure what script it is for custom islands.
I know you can use the value to close the board like we had with classic for guests.
Editing that value in:
cfrm.inc.php
and
portal.inc.php
But to exclude just one custom island I am not sure on.