How many eggs can I put into Isle Avue?
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.