So I think this app I found called Droiditarian does pretty much what you are looking for. I don't think it has that shuffle functionality, but you can always see the list of acts of kindness (they call them "good deeds") so you can choose which one to do for the day. It's actually pretty fun because you can see a map of other people doing good deeds.
Here's the app:
Droiditarian v1.0 Application for Android | Lifestyle