Thank you for using our online answers forum! That's a great question! Unfortunately, SlingPlayer for BlackBerry is no longer supported. Therefore, there are no new applications that are being made. You may be able to use an older version of SlingPlayer for BlackBerry on the PlayBook, however, we cannot guarantee it will work. Here is a link that will take to you the download for an older SlingPlayer version.
Hope this helps!
The Sling Moderation Team