I played there quite often when I lived on Long Island. The nice part about the Bethpage complex is that there are several other courses there as well - Red, Green, Yellow, you get the gist. The Black is certainly the signature track, and very difficult. Carts are not allowed on Black, so be prepared.
If you are traveling a distance to play, my recommendation would be to go on a weekday. Less demand on a Tuesday than there is on a weekend day - thus a greater chance of playing Black. If you can, make it a 2 day event and play some of the other courses there as well. Red is a great run as well. Also, 2-somes are easier than 4-somes, so if you are not adverse to breaking up your group, you will have a better chance of getting a time.
The last option, and I am not a big fan of it, is to purchase a tee time from a travel/golf site and pay a premium to play. I am personally against this type of business, but it would get you on the course.
BTW - Play the tips and bring the long sticks. The course is a challenge!
Good luck and have fun!