Dear Bry_Sinclair,
I wasn't quite quick enough to avoid the first short and sharp reply to this, and I'm afraid it's the sort of question that can come across as trying to poke "oldsters" with a sharp stick. Whilst my preference is not to "harmonise" the two episodes (one happens in an alternate time-stream, so the DS9 people genuinely aren't supposed to be in the original version of events), there are technical issues why they can't be melded, since DS9 can't be made as high-resolution as the 60's filmed "Star Trek". I won't pretend I understand why, though.
The blu-ray boxed sets (assuming you want to go that route) have a veritable tribbleathon, with the original show, the animated series "sequel" and the DS9 episode all on one disc.
Although I can't say so for certain, there may be problems putting the two stories together anyway, since the internal chronology of "Trials and Tribble-ations" is significantly shorter than "The Trouble with Tribbles", at least as far as I've been able to judge.
Timon.