Ad-free angry birds rio for android is free at amazon this feb. the hd kindle tablet version is free as well. Don't know if it works on non-kindle tablets, though.
Grabbed these instructions from a previous Amazon App store bargain (http://www.ozbargain.com.au/node/89155):
Instructions for accessing Amazon Appstore outside of the USA:
http://www.modaco.com/topic/336184-using-the-amazon-appstoreā¦ (Changed the previous link as it doesn't work anymore, similar guides easily found via Google)
You may download the Appstore directly from Amazon by visiting this link from your Android device, rather than risk an .apk from a 3rd party:
www.amazon.com/amazonappstoreapp
You may also need to install and run a VPN to make it look like you are in the USA; try the free TunnelBear VPN.
"We could not process your order because of geographical restrictions on the product which you were attempting to purchase. Please refer to the terms of use for this product to determine the geographical restrictions."
Like others here, my Amazon App account was established with a US address. Is that the problem, or is it complaining that my browser is connected from Australia?