However, the version of Pinky that exists for the quest "A Good Spanking" is tameable.
I thought it was a slightly more unusual tame, even though it's not currently a unique skin/model, and still therefore worth mentioning.This version of 'Pinky' is tameable. Your direhorn is pretty good at tanking, which obviously affects Tame Beast.
However, it's simply a case hitting Pinky a few times to generate "some" aggro and then casting Primal Rage a few seconds before you dismiss your pet and the Juvenile Direhorn dies. Tame away.
If you take too long it's likely the direhorn will respawn and re-aggro Pinky immediately.
This might be achievable without Primal Rage (or similar abilities) but the timing is more luck than anything based on when the direhorn respawns!