Coney Island is a New York City neighborhood that features an amusement area that includes 50 or more separate rides and attractions; it's not a centrally managed amusement park like Disneyland or Six Flags. As a result, specific questions about rides, filming privileges, etc., should be directed to individual businesses.
Coney Island is a seasonal center operating roughly between Easter and Halloween. Rides and attraction are generally open on weekends from Easter until Memorial Day, all week long from Memorial Day until Labor Day, and then weekends from Labor Day until the end of October. The beach and boardwalk are open all year round (although lifeguards are only on duty from Memorial Day to Labor Day) and Nathan's Hot Dogs and the New York Aquarium are open almost every day of the year. The Coney Island Museum is also open on Saturdays and Sundays, from noon to 5 PM all year round.
During the week, rides and attractions may open at noon and run until the late evening. During the weekends, the same rides and attractions open around noon and may run until the early morning.