While not exactly for The Hobbit (but could be), how about an episode of Doctor Who directed by Jackson?
The 11th Doctor, Matt Smith, recently said that he would like to have an episode of Doctor Who filmed in New Zealand — with Peter Jackson.
"Let’s get Peter Jackson to direct one and go and make it in New Zealand," Smith told The Waikato Times (via Blastr). "I would love to, I will campaign endlessly to come over and film there. There’s clearly a great film industry out there. It’s something I would be very interested in, it’s just whether we can persuade the producers to fly us all over."
While the BBC producers of Doctor Who might need some persuasion, The Waikato Times contacted Peter Jackson who needs none at all.
"I’m a huge Doctor Who fan, and I think Matt’s fantastic. Just name a time and place, and I’ll be there!" Jackson is quoted as saying.
An interestingly enough Peter Jackson already has a Doctor connected with The Hobbit, as the 7th Doctor, Sylvester McCoy, plays Radagast The Brown, noted DoctorWhoTV.
We've already seen a Lion, The Witch, and the Wardrobe inspired Doctor Who episode, why not one based on J.R. Tolkien?