This page explains how to get the Oval Charm in Pokémon Sun and Moon, which makes eggs appear sooner at the Pokémon Nursery.

Oval Charm

Go into the building to the left of the Dimensional Research Lab, go up to 2F, and go into the GAME FREAK office and talk to Morimoto to battle him. GAME FREAK Morimoto has a level 62 Kangaskhan, a level 62 Flareon, a level 62 Machamp, a level 62 Dragonite, a level 62 Vaporeon, and a level 62 Jolteon. You get 5952 Pokédollars for winning. Afterward, Morimoto gives you the Oval Charm. Having the Oval Charm in your inventory makes eggs appear sooner at the Pokémon Nursery.