I had a client that asked me to backup his Angry Birds Rio before I reinstall his Windows so..Here is how to Backup Angry Birds Rio:
Step 1 - Find this folder Angry Birds Rio which is located here : "C:\Users\john\AppData\Roaming\Rovio\Angry Birds Rio"
Step 2 - Copy the settings.lua and highscores.lua files to youe backup external drive/ usb stick
Step 3 - To restore it you need to reinstall the game first than search for the folder Angry Birds Rio which is located here : C:\Users\john\AppData\Roaming\Rovio\Angry Birds Rio and copy the files settings.lua and highscores.lua you backed up at Step 2 in here overwriting the files located in there.Done. Start the game and presto you got your saves back.
Hope it helped. Thank you for reading my blog.