All Pokemon that are obtainable in Gen III can be caught in Pal Park. The contents of this answer ignore that.
Venusaur, Blastoise, Alolan Ninetales, Golem, Alolan Golem, Galarian Slowbro, Alolan Muk, Bayleef, Meganium, Quilava, Typhlosion, Croconaw, Feraligatr, Ampharos, Galarian Slowking, Treecko, Torchic, Mudkip, Jirachi, Turtwig, Torterra, Chimchar, Infernape, Piplup, Empoleon, Staraptor, Cranidos, Rampardos, Shieldon, Bastiodon, Wormadam, Mothim, Porygon-Z, Probopass, Phione, Manaphy, Snivy, Servine, Tepig, Pignite, Oshawott, Dewott, Simisear, Simisage, Simipour, Archeops, Meloetta, Chespin, Quiladdin, Fennekin, Braixen, Froakie, Frogadier, Florges, Diance, Hoopa, Volcanion, Rowlet, Dartrix, Decidueye, Litten, Torracat, Incineroar, Popplio, Brionne, Primarina, Crabominable, Lycanroc-Dusk, Type: Null, Silvally, Cosmog, Cosmoem, Magearna, Marshadow, Poipole, Naganadel, Zeraora, Meltan, Melmetal, Grookey, Thwackey, Rillaboom, Scorbunny, Raboot, Cinderace, Sobble, Drizzile, Inteleon, Dracozolt, Artcozolt, Dracovish, Arctovish, Kubfu, Urshifu, and Zarude.
Mew, Celebi, Darkrai, Shaymin, and Victini all require events that are no longer available to be caught. Arceus can be caught through use of an unreleased event.
Source: Cross-referencing the previous answer with Bulbapedia
