Schedule details from a source inside the show (which you can preview here ):

“The Half Hour News Hour”, will premiere on FOX News Channel Sunday, February 18th, at 10:00PM eastern, 7:00PM Pacific.
The following Sunday night (2/25) is the Oscars so FOX News will probably re-run the first show.
The Sunday after that (March 4) the second episode of “The Half Hour News Hour” will air, at those same times (10:00PM eastern, 7:00PM pacific).

The writers of the show are Ned Rice and Sandy Frank, both Republicans. Frank is an Emmy winner (for Late Night with David Letterman). Ned Rice is an Emmy nominee and has been an NRO contributor.