The Cheat from Homestar Runner, and his old-timey cousin, The Sneak. Maybe it's just the art style — the Cheat's baffling physiology probably would make for a pretty horrific-looking creature in a more realistic style.
In Charlie the Unicorn, there is a strange... sea-goat-seal...thing. Charlie even lampshades this. "I can't tell if you're adorable or creepy."
In Protectors of the Plot Continuum, when a canon character's name is misspelled in badfic, a 'mini' creature appears: a small version of a monster from that canon. For Lord of the Rings, Mini-Balrogs, and for Harry Potter, there are Mini-Aragogs, etc. These are cute, but also just as ugly as their larger counterparts.
Fluffy Pony can be this, especially when abusers want to emphasize the oddity of the creatures.
Hellephant on Regretsy (sadly the site has been shuttered), who inspired some adorable fan art despite still being stained and missing an ear.
As hard as it is to believe, there have been times where SCP-682 could be considered "cute", such as his interaction with the benevolent Blob Monster, SCP-999 or his exposure to rage-inducing Creepy Child, SCP-053.
SCP-191 could also be seen in this light. Although in her case its mostly because people feel sorry for her.
SCP-811's description makes her sound like a revolting predatory beast, but her interview log makes her sound like a little child with a cute speech impediment.
SCP-1471a is described as "cute" (in a macabre sort of way) by those affected by SCP-1471 after they get over its Nightmare Face. Keep in mind that it is a shadowy Humanoid Abomination with black hair and a dog's skull for a face that stalks you through texted-pictures and reflections. Its harmless, and is implied to be created as a companion for lonely people, but it is still unnerving to see for some.
The eponymous creature from the Welcome to Night Vale episode "The Visitor", which Cecil initially fawns over as being straight up adorable. However, his description of it is very...odd, with it being vaguely spherical, with stubbly little nubs for limbs are large, staring 'duck eyes', until even Cecil is forced to admit it might not be cute so much as just plain weird. Of course, after what it does to the station cat, its hard to think of it as cute in any capacity.
Rotarr, a character created by Lisa Heschl, is an anthropomorphic housefly. While she's got some Squicky aspects (including an insect tongue and a mottled, gray, hairy body), she's still much closer to a Cute Monster Girl than to Brundlefly.
DSBT InsaniT: Frog, who looks like a green gumdrop with a white circular nose and webbed limbs rather than any sort of actual frog.