Offer people to attach an image to their email address (with verification of the email address.)
We may also want to cache avatars from other platforms as Wordpress uses so we still leave that door open. Always check their terms and conditions (And make a copy of the one we go by) to make sure we can indeed do that.
Our snapwebsites support avatars under the /avatar path (assuming they have the avatar plugin installed). The images are checked on the Snap! Websites first, then external websites such as Gravatar and Avatars.io.