There are groups that can be contracted to take care of the problem.
They come in at night, used low velocity silenced weapons, clean out the deer, clean up the mess, and can be gone before sunup.
None of the faint hearts, except the city fathers, will ever know they have been there.
They are used often in towns full of animal lovers and too many deer.
Actually, on Long Island they bring in archery hunters to cull the deer population because it has grown so much in the densely populated suburbs where there are not any predators(eastern coyote) and houses are too close together(500’) to shoot guns.