Suggestions of cover crop to plant inside the swale? Do they need any? (i'm newbie)

I'm planning on digging a swale for my garden. I havent been able to find any suggestions of plants to plant within the swale. Do you even plant cover crops within the swale? They would have to tolerate being submerged in water on occasion. I don't want to dig a swale just to have it be filled with grasses, that will then drop seed all over my raised beds. and i won't be able to mow a swale down too easy. THanks for any help in advance. Grateful!! blessings.

Beans/peas esp fava beans. Anytype of vines that will cover/shade out any grass that try to grow in the swale. You could plant the vine 1/4 up the garden and then let it run down into the swale.

Thanks a lot!!