I don't know how these things are normally done, but you'd think a private group could do one on its own with its own money if it wanted to, and the group could have a gun dealer handle each transaction so it was all legal. The likelihood of a group of liberal bigots doing something like this with its own money seems small though, since they love spending taxpayer money so much. But with, say for example, the Clinton Foundation having so much money, maybe they could do one.
If they do something like that though, as I said earlier, I think they should include a book buyback too, and see how many copies of the Constitution and the Bible they can get "off the streets," because in the end, those are what the liberal cult really wants to get rid of; civilian disarmament is just a means toward that end. They can get rid of history books that have not been made to fit in with liberal dogma too, and old manuals on grammar and style that were written before liberalism was the official state religion; these books oppress women, because they have sexist language in them (i.e., mankind instead of humankind, etc.). These make every bit as much sense as gun buybacks.