You’re wise to search for plants that are adapted to growing in the wet site rather than trying to change the site or grow something there that isn’t suited for the location. You could perhaps grow a bog garden there if the spot stays consistently moist. If it dries out periodically, your idea of planting a ground cover may be the best solution. Chinese astilbe (Astilbe chinensis), forget-me-not (Myosotis scorpioides), hosta, and fern are moisture-loving perennials that can be grown en masse as ground covers. Lilyturf (Liriope), moneywort (Lysimachia nummularia), and ribbon grass (Phalaris arundinacea) are also good for wet sites.