We don't recommend any turfgrass type for those conditions, because it is not expected to establish and grow well. Turfgrass isn't very tolerant of shade, and is even less tolerant of poor soil drainage or areas that skew wet.

Instead, we recommend you try sedges (botanical name Carex) if you want a grass-like look. (Other perennial and shrub options exist if you don't need the planting to resemble a lawn.) Mt. Cuba Center, a native plant-focused public garden in Delaware, published a guide to native Carex that are suitable for garden use, since our region is home to many dozen native species of Carex. It may come in handy if you'd like to look over the listings for species most tolerant of shade, wetter conditions, and which can handle occasional mowing. (Though that is just for looks, since the plants do not need mowing to thrive.)

Some online native plant suppliers likely sell Carex as seed, though it might be more available as plugs. (Plugs are young plants older than seedlings but younger than the typical pot sizes available at a garden center. They are easier to handle than seed since they have a head start on growth, they establish pretty quickly, and they cost less than anything other than seed, especially in quantity.)

Miri