The Isle Avue lets you put eggs into the hot springs to hatch them. I haven't been able to put in an egg yet since I don't have any. The other islands have different effectiveness based on number of beans. How many eggs can I put in the hot springs for each tier of beans on the island?
From pokemongohub, it looks like this is the breakdown of Pokémon or eggs per level:
at Tier 1, you can place 6 Pokémon or eggs.
at Tier 2, you can place 12 Pokémon or eggs.
at Tier 3, you can place 18 Pokémon or eggs.
Thus, regardless of whether you put in Pokémon or eggs, the cap is the same.