Possible solutions:
1. The government can hire hunters to kill the deer, and donate the venison to soup kitchens (as is done elsewhere). Allowing amateur hunters to hunt in suburbs would be unwise
2. The frum community can get permission to capture the deer, leading to a kosher venison industry
3. Based on common law, the crown owned the deer and those rights went to the states, so the deer are owned by the state. And, New York is an infamous “nanny state” known for rather ridiculous projects to waste taxpayer money. So the state can round up the deer, force them to listen to road safety lectures. and release them wear yellow safety vests. This idea might appeal to someone such as De Blasio if he manages to get elected governor.