I'm running under the assumption you are looking to download Slingplayer on your wife's tablet. You should not need to pay for the app twice. The purchase has already been made in the Google account you made the purchase under. All you need to do is purchase the Slingplayer app in the Google Play Store using that same account that you used before on the other device.
If you use the same Google account you originally used to try and purchase the app on the other device (your wife's), and it still tries to charge you, then you'll likely want to reach out to Google, because the Play Store should not try to charge the same Google account twice for the same app.
Also, do make sure it is the same app, as there is one for tablets, and a different one for phones. The Slingplayer for Phones app works on both tablets and phones, while the Slingplayer for Tablets app will only work on tablets.
Hope this helps!