In answer to the OP's question, there's a few, but a limited number of them. Most of what's been found, and or indexed by the existing deep web search engines have already either been abandoned, or been taken down by their original authors.
What's interesting about the few places I've been that are somewhat still active (1-6 people is your best average of any furry website on the deep-web) is that more than half of them are really just more private live journals. Not the same software or design, but in principle, the same idea.
Other furry websites on the deep-web, though limited, serve the purpose of art way-stations for websites that require that you pay to access their content. Again, most of these websites have already collapsed as the need to use VPN's to find anything "furry related" was a fools errand, and the cost of accessing these sites for whatever bland content was there had poor loss-to-gain relationships in terms of access time and what was really being offered.
Nothing was new, and anything that could be offered somebody else already had. In many respects, and this is a blessing, the deep-web for furry related crap is dead. Which is to say, that nothing new and nothing that is new really goes onto these private websites at all. And that really goes for every website out there on the deep-web.
That's where the shit gets good.
I can't imagine what else is good about these sites apart from ... what? The edgy card people get to play in knowing they're there?
Just listen to Rush Limbaugh x Alex Jones squared preamble as mumbled by Joe the Plumber, or an Alabama Klansmen = 89% of the deep web.