If you have purchased the SlingPlayer app from the App Store and are logged into the same account (Apple ID) that you used to purchase the SlingPlayer for iPad, the app should be accessible for you to install on your new device. SlingPlayer for iPad can be installed on up to ten iOS devices, so long as each device is associated with the same iTunes/App Store account (Apple ID).
You could also try this:
If the problem persists beyond that, I would advise contacting Apple directly as they can assist you with your App Store purchases and management of your purchases.
The Sling Mod Team