South Huntington Town Range on Long Island (you don't need to be a resident to shoot there) used to let you use shot on the rifle range (50 yard);
Nassau County Range (also Long Island) used to allow you to shoot anything but FMJ (shot might beat up their target hangers, not sure).
I don't know if either of these ranges have changed, I haven't been there in years, but all the rifle ranges I have been to let you shoot shot as well.