The prevailing wisdom is that country-rock (not to be confused with alt-country, Americana, y'alternative, or later labels) emerged in the late '60s, more or less simultaneously with the releases of The Byrds' Sweetheart of the Rodeo, Dylan's Nashville Skyline, The Nitty Gritty Dirt Band's Will the Circle Be Unbroken, and the brown album from The Band.
Conventional wisdom has apparently never heard The Dillards, who were mixing up banjos and backbeats in the mid-'60s. Brothers Rodney (guitar, vocals) and Doug (banjo, vocals) Dillard migrated from their Ozark Mountain home to southern California (and from there to multiple appearances on The Andy Griffith Show) in the early '60s, playing a relatively straightforward brand of bluegrass. But by 1965, at the height of Beatlemania, the brothers had discovered a potent mix of bluegrass standards, soulful, mystical originals, and Lennon/McCartney covers. By 1968 the transition was complete, and the resulting album Wheatstraw Suite is an unheralded classic -- arguably the first country-rock album, a wondrous collection of traditional bluegrass instrumentation, pedal steel, and unmistakeable backbeats courtesy of drummer Jim Gordon, shortly before he hooked up with Eric Clapton and Duane Allman in Derek and the Dominoes.
It was a direction that spooked Doug Dillard, who quit the band to join ex-Byrd Gene Clark in Dillard and Clark. Ironically, Dillard and Clark produced their own brand of country-rock shortly thereafter, penning several songs that would become classics of the genre, and that don't sound remarkably different from the contemporary work of The Dillards. Go figure.
For an excellent overview of the evolution of a great band, pick up There is a Time, a Dillards compilation that spans the years 1963 - 1970. Listen to the harmonies and hear the template that bands such as The Eagles and Poco would smooth out and take to the pop stratosphere in the following years. Rodney and Doug deserved better. To quote Lebowski, "I had a rough night, and I hate the f*&%in' Eagles, man." Me too.