First, let me say that you can have a nice yard and garden and ducks. I have it all!
Next, it takes some planning and understanding ducks.
For example - I have a beautiful kiwi arbor. The plant is on the other side of a fence from the ducks, and climbs up cedar posts to form kind of a grotto when the leaves are out. The ducks can enjoy the shade underneath. Some of the vines hang down, and the ducks can nibble on the leaves - but most of the plant is out of reach. In the fall, when the fruits fall, the ducks can eat them.
Blueberries are nice, very pretty, and though the ducks will eat the blueberries they can reach, they cannot reach most of them.
I plant pots with greens (mild mustard, cabbage, kale, and clover), and when they are an inch or two high, I put the pots into the pen and just let the ducks nom them to the dirt. I pull the pot, replant, and in a few weeks, let them play again.
They generally eat down tender annuals pretty quickly, and they don't mess with woody perennials as much. Knowing those things, I am able to have a yard that they enjoy and that I enjoy.
Oh, I have netting over part of the tea garden (fenced in for the ducks). Last year I let some wild grape climb over the netting. It provided shade, and little bunches of wild grapes hung down into the pen. The ducks ate some, and I ate some. Yummy.
Just thought of some other of their favorite plants.
Comfrey - they like nibbling on the leaves, and comfrey bounces back quite well. I even grab a handful of the coarsely hairy leaves, rub them between my hands to soften them a little, and toss that into the swim pan - nice treat
Myrtle (Vinca Minor) - tough little evergreen groundcover - pale purple flowers in the spring.
Daylilies - can be nibbled, and provide nice cover when full grown. These are perennials. If you were closer I would give you a dozen or two.
Comfrey, Myrtle and Daylilies are vigorous - they spread, slowly or quickly (depending on the person's sense of time), and some folks don't like having to keep up with thinning them out. But the ducks do a pretty good job, actually. My Runners ate down an entire patch of comfrey when I let them spend too much time in that garden too early in the spring.
Timing matters - Once plants get to be about a foot and a half tall, they are less likely to be eaten down.