Phrase or idiom for "vocal minority"
The translation for 'minority' is straightforward: 少數派. Note: not 小數派 (少 refers to little in quantity, 小 refers to little in (physical) size). To be concise, you may say 少數.

For 'vocal', 敢言的 or 直言不諱的 (see here) are translations that give it a fairly positive light. Tang Ho's answer 積極的 is neutral, somewhat positive.

發聲的 is a literal translation but understandable (I for one think it is understandable, given that you're not translating the term alone but with a wider context). A neutral alternative, albeit slightly weak, is to say 不沈默的少數 which makes deliberate reference to its antonym 'silent majority' (沈默的大多數). I also found a third neutral translation, 說話大聲的少數族群, in a book on journalism published in Taiwan1, where vocal minority is contrasted to the disadvantaged minority. Finally, I find the neutral translation 喊叫的少數 made by the Taiwanese politician James Soong in one of his works2 the most idiomatic of them all.

If you want to be outright negative (considering the fact that vocal minority can be euphemistic), you may consider the idiomatic saying 一小撮人的意見 (lit. the opinion of a handful of people), but this is not a direct translation and is quite dismissive. A Japanese political publication3 gave the translation うるさい少数派 (a possible Chinese translation: 嘈吵的少數 'noisy minority') which I think is best in delivering the negative nuance.


1 何日生（2007）《建構式新聞》。台灣：五南，頁175。
2 宋楚瑜（1978）《美國政治與民意：兼論中美關係》。台灣：黎明文化，頁51。
3 信田智人（1996）『官邸の権力』筑摩書房 pp. 230