I was born considerably before 1987 and still the quote escapes me. Perhaps you logic is flawed in assuming only Trekkies recalling one specific quote were born before 1987. I will have to laugh at the irony if somebody younger than 22 answers your question correctly.
Same here. Born along time before then. Even my baby brother is older than that rofl. And I have never heard that quote or recall it if I did hear it. But considering there were, as far as I recall, 2 tribble episodes. The original series and DS9 I would vote it being the DS9 one. Sounds like something worf would say