By far, the largest collection of Jolson movies is held by Turner Broadcasting. Many of the early movies have aired on the network, as well as the Plantation Act short. Feel free to drop them a note, thanking them for their past attentions, and requesting future screenings of Jolson movies.
Cinemax does not have a lot of Jolson films, but they do appear to have both The Jolson Story and Jolson Sings Again. A note to them to request screenings of these films may not hurt, either.
Both Bravo USA and Bravo Canada have aired the wonderful South Bank Show, the closest thing yet to a television biography of Al Jolson. They have also shown The Jazz Singer! Click on either network's name to request a screening of that show.
The A&E Biography show has indicated interest in an Al Jolson biography, but has not promised anything. Continued input to them may help promote a Biography of the World's Greatest Entertainer. Click the "Programming" button at the bottom of the page linked to for your suggestion.
The new MSNBC Cable show, Headliners and Legends, has expressed an interest in a program devoted to Al Jolson who was, after all, an NBC radio headliner in the 1940s, and clearly a legend. Drop them a note and encourage them in the effort!

The Encore Channel has played both The Jolson Story and Jolson Sings Again, so we know they have them! Why not drop the network a line, thank them for showing the films, and ask for future screenings?
