Many types of cherry trees are known to produce suckers, such as chokecherries and Canadian red cherries. Suckers are not just unsightly, but they use nutrients and water that the cherry tree needs to thrive. Unfortunately, suckers are difficult to control; and while it's possible to stop or inhibit their growth, without constant attention, they will sprout again, or new ones will grow.
Remove the cherry tree suckers before they reach 20cm / 10 inches in length. Cut them off with pruning shears or a hand saw. Many grow from the ground so dig down a bit to cut so you are not left with little stumps that interfere with foot traffic.
Spray the point at which you cut the suckers with a chemical product made to prevent sucker growth, also known as a plant growth regulator, napthaleneacetate (NAA). This will help prevent regrowth in the same spot for three to five months.
Cover the area with thick plastic sheeting as an alternative to spraying the stumps with NAA. Then cover the plastic with 6 to 9 cm / 3 to 4 inches of mulch. This will help stop the suckers from growing, but more attention will need to be paid to watering the tree. Remove the plastic every week or two and water the tree with 2cm / 4cm or1 to 2 inches of water. Remove the plastic in the fall when sucker growth is less of a problem. Replace the sheeting in the spring if necessary.