The story is usually told like this:
Plato presented a theory of ideas, saying that there were many different cups in this world but only one idea of a cup, a "cupness" that comes before the existence of cups. Diogenes said, "I can see cups on the table, but I can't see the cupness." Plato replied, "that's because you have the eyes to see the cup, but not the intellect to see the cupness."
Diogenes picked up a cup and said, "Is it empty? Where is the 'emptiness' which precedes this empty cup?" He reached over and tapped Plato's head, saying "I think what you will find here is the emptiness."
It's pretty hilarious and several people have posted it. But where does it come from?
Well, the first half is from Diogenes Laërtius, Lives of the Eminent Philosophers, Book VI, chapter 53:
As Plato was conversing about Ideas and using the nouns "tablehood" and "cuphood," he said, "Table and cup I see; but your tablehood and cuphood, Plato, I can nowise see." "That's readily accounted for," said Plato, "for you have the eyes to see the visible table and cup; but not the understanding by which ideal tablehood and cuphood are discerned."
(source)
But there's nothing here about Diogenes' riposte about emptiness.
I couldn't find any other historical source. I tried sorting my Google results by date and the oldest ones are these three (all of them dated Feb 1, 2001 although I doubt they were all posted on the same day; it must be the day they were indexed by Google or something). I can't open the PDF file and the other two don't list a source, either; they consist of anecdotes of which some are also from Laërtius, but others seem suspicious.
So is it fake? If so, I find it fascinating (given the unreliability of even ancient sources about Diogenes) that people would come up rumors and legends about this man even in the modern age.
Hoax or not, if someone here has the original source of that particular anecdote about emptiness, I would really appreciate it.
Well, this was a merry tour of the recesses of the Internet!
I began by repeating the search you already made. The first thing that struck me is how many people have copied the story across the web, often rephrasing it, but without ever changing or adding to its elements. As you already noticed, there doesn't seem to be any further ancient source behind it. The anecdote must therefore be a modern elaboration on Diogenes Laertios 6.54, which hasn't existed long enough to pick up further embellishments.
Google yields the most likely culprit: Michael Boylan and Charles Johnson (eds.), Philosophy: An Innovative Introduction: Fictive Narrative, Primary Texts, and Responsive Writing (2010, reprinted 2018). This book uses short fictional stories as a way to introduce and teach philosophical concepts. One of its stories, 'The Cynic' by Charles Johnson, is told from Plato's perspective; it includes the anecdote in Diogenes Laertios, but then extends it with the exact riposte you've found elsewhere. It even gives us the pacing and phrasing that is common (with minor variations) to most of the versions this anecdote takes online.
It seems pretty obvious that this didactic fiction is the origin (and the reason) behind the extended anecdote. It is not historical. It does not occur in this form anywhere in the sources, and does not occur anywhere on the internet in a form that is demonstrably independent of Johnson's story.
The only problem is that you found three websites apparently dated to 2001, nine years before Boylan and Johnson published their story. However, as you said, the dates are all identical and this seems to be an issue with Google. When you go to the actual page and check the page info, you find that this one was actually published in 2015 and this one was first published in 2013 but edited as recently as 2018. The only one I couldn't verify was the broken PDF, but the pattern seems clear enough to assume that one also postdates 2010. If you change the Google search to show all results up to 31 December 2009, it adds only one page, which was published in 2009 but edited in 2018.