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I've been looking for the origin of the 'particle zoo' expression but so far failed to track down who first used it or at least who popularized it.

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I suspect if the witticism had been associated to a specific individual, we'd be hearing more and more, and also competitive attributions to it. Oppenheimer (below) had a yen for adopting catchy expressions.

It was an obvious one, in the 1950s, after the discovery of mesons, hadronic resonances, hyperons, and on and on. The new accelerators and technique made possible the sudden proliferation of particles, so that there was an acute classification issue developing, akin to that of the Zoologists--or Mendeleev's.

In Strange Beauty: Murray Gell-Mann and the Revolution in Twentieth-Century Physics (1999) by George Johnson, p 222, you can read

“If you run out of Greek letters, you can always use the names of Pullman cars,” Von Neumann said at the time. Oppenheimer provided the name that stuck: the subnuclear zoo.”

p 755

[footnote 108]: Oppenheimer coined the term "subnuclear zoo" in a public lecture at the Rochester 6 conference, [Sec VIII p1 of the proceedings]

p 337

Finally, as the 1950s drew to a close, there was a deep feeling that an understanding of how the forces were related would point the way toward categorizing the dozens of different particles that continued to pour from the sky and accelerators in a random spray. Oppenheimer talked about the subatomic zoo, but physicists had hardly begun putting the beast in labeled cages ...

Rochester 6 took place in 1956.

Of course, the biography deals with the "Mendeleev" and, remarkably, in short order!, the "Henry Moseley" of hadrons, among other things, namely the tabulator, classifier, and then explainer of the reason behind the pattern: quarks.

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