A good one for partial sunlight is impatiens. They are what I have to use under a tree of mine because nothing else will grow there and they actually do really good.
Bleeding hearts, forget-me-nots, curly mint, Japanese painted fern, coral bells, Korean angelica,
Dalmation bellflower, blue comfry, Labrador violet, and geranium striatum are some good border plants.
Give forget-me-not a try they are happy in full sun to partial shade. They grow 6 to 8 inches in height. Ball shaped plants are massed with indigo blue flowers. The plants reseed freely if the spent flowers are not removed. They must have moist soil and prefer a cool location.
Hostas are good plants to use as a border; they thrive in partial sun/partial shade and need very little care. They are perennials that send up a flower shoot during the summer. The plant has large, very nice leaves.