Spring: Children's Zoo / Education pack
Dwarf goat, muscovy duck/wild turkey, rabbit, either coati or small monkey (squirrel or tamarin)
Summer: Americas Pack
Howler monkey, coati or small monkey, ocelot, rhea/wild turkey/muscovy duck/Canada goose, NA porcupine, musk ox, walrus
Fall: Feather pack
Grey crowned crane, secretary bird, shoebill, burrowing owl
Winter: Alpine pack
Spec bear, hyrax, gelada/baboon, markhor, pheasant, pallas cat, big horned sheep/aoudad, tree kangaroo
Unlikely, but I think it would hit most of the remaining top animals. Blackbuck, ABB, spider plus old world monkeys, and serval were the main high rankers I couldn't wedge in, but I also didn't fill an anniverary spot so... / denotes multiple animals who could fill a similar spot.