When did the conservative "liberal media" meme get started ?

[JHB]

10. Depends on how you define "start", but...

...the current strain of it can be traced Buckley, Goldwater, and those who rallied around them.

For example, from McCarthy and His Enemies (1955) by William F. Buckley and L. Brent Bozell Jr. (father of the Media Research Center guy, naturally). Bozell was a speechwriter for Goldwater.

Perhaps McCarthy deliberately sensationalized the evidence he
possessed in order to draw attention to the gravity of the situation .
Perhaps, again, the complexities of the Communist problem were
lost on Joe McCarthy in the early days of his venture . After all, he
had seen alarming reports of various investigating agencies on certain
employees of the State Department . And who, McCarthy may
have asked himself, who but Communists would do and say such
things? That only Communists would so act is perhaps a logical
answer to the question ; but logic in our age, must be strained
through the woof of irrationality and the warp of ignorance . Many
non-Communists behave in a baffling manner, and McCarthy
should have taken this into account-all the more since he was prepared
to challenge the President of the United States, the political
party in control of Congress, and the vigilantes of Liberalism in the
press and the classroom.

There's plenty of other things which would take too long to post right now, but suffice to say their view of the press was a liberal version of what FOX News actually is. Any setback (like Goldwater's loss) could be blamed on liberal media bias.