Any manga where a human female, or human male, protagonist falls for a male furry (anthropomorphic man)? And I don't just mean ears and tail, I mean they are furry from top to bottom. [Please, no hentai, but everything and anything else is okay. ]
That's really all the specifications I have.

An example? Something like Koketsu Dining.

Wow, that's a toughie.......sorry, the only mainstream one I even know of with furry type characters is Carnivorous Princess Yegrinna, but I have no idea if it meets the rest of your requirements (cuz I waited for it to be completely scanlated before I read it and still haven't gotten back to it >_<)

I think the category you'd be best to look for is "Anthropomorphism" (if you didn't already know that) ..... I did a search with that and "romance", there's not much, but you could take a look through that.

https://www.mangaupdates.com/series.html?category=Anthropomorphism& genre=Romance&perpage=50

Good luck finding something

Awesome. I'll go check it out! ^^

Unfortunately, I have tried that, but the results aren't what I was looking for. Its either about an animal who turned human or a human with ears.
Sad, but true.

I'd guess that's your cue to broaden your reading horizons then

Hey, it happens, getting locked into one demographic/genre/type/theme always ends the same way.....you run out of things to read

You might want to check out the Kemono/Jingai BL anthology.

Also, Odette.

I also have some recommendation for non-romance manga in this genre/theme if you're interested.

You might like koalove. it's mostly comedy and it's not Sure yet if It Will become romance or not, though.

Ookami Ningen to Ningen Ookami - You should probably keep an eye out for other stories by Nagabe.

Mononoke, a short story by Hayao Miyazaki from 1980. (Sort of a precursor to Mononoke Hime; it isn't listed on MU.)

You might also enjoy Ode to Kirihito.