Dig or pull cotoneaster in spring when the soil is moist and the fruit hasn't yet ripened. If the plants are too large to pull or dig, a backhoe may be needed. Be sure all roots and stumps are removed to prevent resprouting, and then replant the area with noninvasive native plants to prevent cotoneaster from re-establishing.
Smother young cotoneaster seedlings by covering the area with a double or triple layer of plastic sheeting. Extend the plastic sheeting at least five feet beyond all sides of the problem area, and then leave the plastic in place for a minimum of two years. Once the plastic is removed, plant a noninvasive ground cover.
Spray cotoneaster with a herbicide such as glyphosphate if other removal techniques fail to eradicate the plant. Apply the product strictly according to the manufacturer's directions on the product label. Spray only on a quiet day, as spray drift is harmful to nearby plants and people.