I think that Discourse has essentially been using Facebook’s emoji set until recently, or at least that’s what we’ve been seeing and what the URL for an emoji like 
would seem to indicate: https://emoji.discourse-cdn.com/facebook_messenger/frog.png?v=14. Looks like they made some recent changes because of licensing issues. Since the facebook_messenger set now translates to Unicode, the frog will appear however a particular user’s OS/fonts render it. I suppose that a motivated forum user could create a poll and/or petition the administrator to change the set, maybe by posting to the Forum Operations Feedback Thread, since administrators can change the set that a Discourse instance uses. Just like with the
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