After seeing the video it's obvious they don't need us to set up a tank for them.
While your original idea was thoughtful public aquariums need to have the funding to run an operation like this. NY Aquarium does have financial issues as they do make appeals to the local aquarium clubs for funds to buy things as simple as chairs never mind the large purchases of equipment that setting up a reef tank requires.
The Brooklyn Aquarium Society is based out of the aquarium in Coney Island and they have ALWAYS been willing to help them with anything that would be needed for both FW & SW set ups. The BAS has set up many tanks around Brooklyn in the public school system and provides ongoing support for them. You might want to join that club and volunteer to help with the tank set ups that they do handle at the schools
Calling the aquarium would be a nice idea to inquire if they would be interested in coral donations, but I doubt they would be looking for the little 3/4" frags that some would consider a donation, but best to ask. Colonies would be more in line with what they might require and public aquariums - even places like Atlantis - do trade corals between each other to add to the varieties they keep
As far as donating fish - NO fish would be moved from your home tank straight into their reef tank...it would be QT'd first IF they even chose to accept the fish at all. Unfortunately public aquariums get MANY calls from folks looking to 'drop off' their fish when they get too large and do keep in mind many of those people making the calls are not on sites like MR, there are many who don't chat on forums but who do purchase fish without considering their eventual size. I'd hope the people who regularly read MR would NOT be buying inappropriately sized fish in the first place that they know will outgrow their systems as too many of those fish end up dead.
That is truly a waste and public aquariums do quickly become saturated with large fish which is sad.
Sorry to be another Debbie Downer, but that is how it is out there...