We know that Tribbles are born pregnant. From The Trouble with Tribbles:
McCOY: "Well, the nearest thing I can figure out is that they're born pregnant. Which seems to be quite a time saver."
KIRK: "I know, but really..."
McCOY: "And from my observations, it seems they're bisexual, reproducing at will. And, brother, have they got a lot of will."
Do we know anything more than that, either from statements in another episode, a Star Trek book, or a statement from Roddenberry, Gerrold, a cast member or other similarly knowledgeable person?
Consider: You have a Tribble on your lap; call it (her ??) T-zero. Fairly soon, T-zero produces a Tribble kit, T-one. We know T-one is born pregnant with T-two. But when does T-two become pregnant?
I've ignored litters, but the question is easily generalizable to litters.