It seems only the preorder Rivera and bonus Tribbles Photonic and Assimilated Borg Tribble are working.
I use the later 2 with my klingon toon.
Technically none of them should work at all. Tribbles and Klingons are mortal enemies, a result of the Klingon-Tribble war where the Empire decimated the tribble home world Iota Geminorum IV. So if they actually follow canon then NONE should work, including the bonus ones. But AFAIK, only the non-breedable bonus tribbles have worked in my experience.
The one canon exception I can think of is the Borg tribble where its assimilated and well could have its emotions/will subverted by the Borg implants. This tribble is already a stretch as it is as I know of no other example where the Borg have assimilated any non-humanoid. So, I guess they can stretch it a bit more and have it like Klingons too.
I got a bit of an issue... I play as a Jem'Hadar, and several of my BOs are as well. Anyway...
Somehow a few tribbles got into the Ketracel White... and they ate a crewmen who went into the cargobay to see what all the roaring was. Anyway all the White is gone, the Klingon crew refuse to leave the station, and did I mention the white is gone?