Caterpillars of many moths and butterflies eat Black Cherry leaves, including: Eastern Tiger Swallowtail, Viceroy, Red Spotted Purple, and Painted Lady. Eastern Tent Caterpillars can often kill Black Cherry trees by eating most of the leaves.Some fungi which are parasites Black Cherry trees include: Honey Mushroom, Tinder Polypore, and Chicken Mushroom. White-tailed Deer, Eastern Cottontail, mice, and Meadow Voles all eat Black Cherry seedlings.aterpillars of many moths and butterflies eat Black Cherry leaves, including: Eastern Tiger Swallowtail, Viceroy, Red Spotted Purple, and Painted Lady. Eastern Tent Caterpillars can often kill Black Cherry trees by eating most of the leaves.