I had good luck with mim clover, crimson annual clover and a northeast usa cover crop blend in my duck area. It was fill dirt before it was turned into a duck area so there wasn't any greenery. do have bare spots this year but I don't think the ducks caused those.
I'm over planting with sorghum grass (which loves muddy and wet conditions) and a northeast forage mix for livestock. Sorghum grass can grow very tall.
Other plants i know my ducks enjoy eating: watercress, dandelions, those cornflower blue flowering plants (i'm having a brain fart and I don't remember what its actual name is), dock, sorrell, thistle, chick weed, mint... I'm sure there are others.