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" in English is senza coda("without tail") in Italian.
hamster
Pika
The island with tailless cats is called Isle of Man, located in the Irish Sea between Great Britain and Ireland. The cats from this island are known as Manx cats, and they are naturally tailless or have short tails.
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.
Apes
toad
barbary ape
Erm... Probably a rabbit.
The tailless cat, Manx, is from the Isle of Man.