I've love to know if this is possible as well.
This might not help now but we have a badge in our community for those who update their avatar so to get an idea of how many updated we can use LSI's Badges report. Beyond this I don't how how to get that information, perhaps via the API?
While this isn't a solution to avatar reports, your idea of creating a badge then run a report for all users that earned that badge within a certain date range is a workaround. Thank You!!
Oh geez @tyw - I like your style. That is some serious h4x to get a specific report. Props.
To award a badge when a user changes their default avatar image, use this syntax:
avatar_change = true
Note: At this time, this badge is triggered only when the user chooses/uploads their own avatar not, not if they change it to another image in one of the community avatar libraries.