Sony have announced that F.E.A.R. 2 - Project Origin demo on PlayStation 3 owners will be releasedexclusively with Qore. You'll have to buy the forthcoming episode of their downloadable video magazine.
According to DarkZero, the show and demo will be coming "mid-January," so that could presumably be as soon as late next week. Single episodes of Qore cost $2.99, with a 13-episode subscription costing $24.99.
There's no word yet of a potential F.E.A.R. 2 demo on the Xbox 360, which obviously wouldn't carry any similar restrictions. The game is set for release for the Xbox 360, PlayStation 3, and PC on February 10.