Remove the weeds and debris from a new planting area with good-draining soil in full sun exposure. Loosen the soil to the depth of 6 to 12 inches with a shovel. Break up large dirt clumps. If drainage is a problem, then mix in a 3-inch layer of well-rotted compost. Rake the prepared planting site smooth and level.
Dig up the established patch of “Moonbeam” coreopsis. Push the shovel under the plants and lift up. Remove the flower roots from the soil. Shake part of the soil off the roots and separate the spidery roots.
Dig a hole with a hand trowel in the new area as deep as the roots. Spread the roots out in the hole and cover the roots with soil. Firm the soil gently around the roots.
Space the rest of the coreopsis plants 12 to 24 inches apart. Water the area thoroughly until the top of the soil is a bit muddy. Replant the parent plant roots in the old location and water.