Challenge accepted:
Pinnipeds are 3 families, we already have a sea lion and a true seal, so the 3rd would be the walrus. It would also represent the polar seals.
Bears, I love them, but we already have enough. We just lack 3 species (sloth, spectacled and black American) and none of them would give us any different from the 6 we have, specially the black Asian and the sunbear.
Goats we have from America and a Europe, so the 3rd one from Asia. Takin or markhor, I guess... Thar or serow if they want something less common. There are other Asian and African candidates but they would be too similar to the ibex or the sheep we already have.
Boars, or pigs, or hogs, or suids... We have jungle Asian and grassland African, both tropical, so I wouldn't bet on red river hog (even though lots of people loves them including me) as it's jungle African. I guess wild boar from temperate Eurasia or collared peccary from America (although they are more related to tropical forests than to deserts or temperate climate).
But you got me with Mustelids, I don't know... They are maybe the most diverse group from the list, and I think some of them are too small (weasel, stoat) or too arboreal (marten, tayra) for Planet Zoo.