This is the big-picture right answer and we should treat this paragraph as gospel.
Here's how to have an impact on the local Sinclair stations: first, watch the station and make a list of all of the local advertisers. Then, write to the sales manager -- not the general manager, but the sales manager -- and tell him that you're going to contact all of the local advertisers to register a protest about the station airing this program. Be specific -- mention the names of those local advertisers. Then, actually contact them (if you write or email, cc the sales manager). These stations make most of their income (around 60%) from local advertisers and will NOT want to have that income threatened.
http://www.talkingpointsmemo.com/
Added: This part below is not gospel, but it's one man's idea of a letter to a local advertiser. (Critique encouraged):
It has come to my attention that <company or business name> currently advertises on <TV station>.
As you may be aware, <TV Station>’s parent company, Sinclair Broadcasting Group, has ordered <TV Station> to air a political program entitled STOLEN HONOR in prime time before our upcoming elections. This is not paid political advertising. This is a gratis airing of a TV program produced by political partisans for the sole and express purpose of slandering a particular presidential candidate and besmirching his sterling service record as a decorated US combat veteran.
I realize that you do not make programming decisions for Sinclair Broadcasting, but you are nonetheless a tacit supporter of a distinctly un-American abuse of the public trust that we, the people, have extended all broadcasters. As such, you will be subjected to considerable negative publicity and will be targeted by national and local boycotts.
<company or business name> may be individually blameless, but Sinclair Broadcasting Group's political abuse of our public airwaves cannot be defended and the net of public outrage will ensnare large and small fishes alike. I will be joining in all boycotts against local advertisers on all Sinclair Broadcasting outlets, including a boycott of <company or business name>. I will also be encouraging every person I know to join in the boycott and will be distributing calls for a boycott of <company or business name> through flyers, letters and internet postings.
Respectfully,