I'm guessing here- guinea pigs or cavies fit the criteria.
Tailed Tailless Bat was created in 1818.
there are many kinds so maybe you means some of these. moderate bobtail hairless semi-cobby longhair curly semi-foreign tailless moderate shorthair svelte cobby brachecyphalec (where nose is close is eye level, ex persian)
Tailless dogs are those dogs which have a small tail or no tail.
"Tailless" in English is senza coda("without tail") in Italian.
hamster
Pika
Not all frogs or toads tailless as adults. There are two species that do have them. The Tailed Frog is able to survive in extremely cold water.
The tailless primates that are most like humans are bonobos and chimpanzees. They share a close genetic relationship with humans and exhibit complex social behaviors, tool use, and problem-solving abilities similar to humans.
toad
barbary ape
Apes
Manx or tailless cats are from The Isle or Island of Man. They are thought to have been left from Ships of the Spanish Armada, as early as 300 years ago.