Is 'calm' an accepted meaning of 'docile'?
The most recent editions of Merriam-Webster's Collegiate Dictionary and The American Heritage Dictionary of the English Language offer no support for the proposition that "calm" is an established meaning of docile. From Merriam-Webster's Eleventh Collegiate Dictionary (2003):
docile adj {L docilis, fr. docēre to teach; akin to L decēre to be fitting more at DECENT} (15c) 1 : easily taught {a docile pupil} 2 : easily led or managed : TRACTABLE {a docile pony}
In the same dictionary, a usage note comparing docile to obedient, tractable, and amenable offers this further gloss on docile:
DOCILE implies a predisposition to submit readily to control or guidance {a docile child}.
And from The American Heritage Dictionary of the English Language, fifth edition (2010):
docile adj. 1. Ready and willing to be taught; teachable. 2. Yielding to supervision, direction, or management; tractable. {Latin docilis < docēre, to teach ...}
The narrowness of these definitions does not, of course, mean that people in the wild never use docile to mean "calm"; but it does give a strong sense that such usage is relatively recent and/or rare. If the usage catches on, dictionaries will eventually include the new definition in their entries for docile, but assessing when a meaning has sufficiently caught on is obviously not an exact science.
In the case of docile as "calm," the biggest impediment to acceptance may be that proponents of the new definition have not yet overcome lexicographers' presumption that speakers intend docile in an already established sense—specifically the sense of "tractable" (that is, manageable). In the example in the posted question—
After having been offered complimentary drinks, the customers grew [became?] docile.
—it is certainly possible to read the situation as involving customers who were restive to a point verging on unruliness, and that the round of free drinks restored order and made them manageable once more. In practical terms, their becoming manageable coincided with their calming down—the two things are closely linked in this case—but that doesn't mean that the writer intended docile to mean "calm" rather than "tractable."
Because the Eleventh Collegiate's usage note asserts that docile properly indicates a predisposition to submit to control or guidance, we might argue that it isn't a good word choice in the cited quotation—that a word like cooperative or complaisant (or calm) might be more technically accurate. But on the other hand, "Yielding to ... direction or management" seems to fit the case rather well. Beyond all this, people use words loosely (and without consulting a dictionary) all the time. The unanswerable question is, when do enough people use a word in the same previously non-approved way to give it legitimacy as a new meaning of the old word?
When did 'tractable' emerge as a dictionary-approved meaning of 'docile'?
I was curious about when the original "teachable" meaning of docile expanded to include the later "tractable" meaning, so I checked a bunch of old dictionaries to see what they had to say about docile. The expansion in meaning occurred earlier than I had imagined.
The earliest English dictionary to cover the word is John Bulloker, An English Expositor: Teaching the Interpretation of the Hardest Words Used in Our Language (1616), which acknowledges only the "teachable" sense of the word:
Docill, Easie to bee taught, one that wil soone learne.
Docilitie, Aptnesse, quicknesse of vnderstanding.
A half-century later Edward Phillips, The New World of English Words (1662) indicates that little has changed:
Docility, or Docibility, (Lat.) aptness to learn that which is taught.
But Elijah Coles, An English Dictionary: Explaining the Difficult Terms That Are Used in Divinity, Husbandry, Physick, Philosophy, Law, Navigation, Mathematicks, and Other Arts and Sciences (1676) shows the beginnings of a new meaning:
Docile, teachable apt to learn.
Docilize, make tractable.
Elsewhere in the same dictionary, Coles defines tractable as "easie to be handled." To judge from Coles, then, docile in the sense of "tractable" emerged obliquely, through the verb form docilize. The next phase in the emergence of the new meaning of docile appears in John Kersey, Dictionarium Anglo-Britannicum: or, A General English Dictionary (1708):
Docible or Docile, (L.) Teachable, apt to learn.
Docility, Teachableness, Tractableness.
On one level, Thomas Dyche & William Pardon, A New General English Dictionary (1735) seems to pull back from the "tractability" angle:
DOCILE or DOCIBLE (A.) Easily taught, that learns without Difficulty, capable of being instructed.
DOCILITY (S.) Easiness to learn or be taught, Quickness of Apprehension, Readiness of taking or conceiving Arts and Sciences.
But on another level, "capable of being instructed" suggests not an aptitude but a condition of mind—and one not terribly distant from that implied by tractable.
It remains for Samuel Johnson, A Dictionary Of The English Language (1756) to complete the identification of the new sense of docile:
DOCILE. a. {docilis, Latin.} 1. Teachable ; easily instructed ; tractable. Ellis. 2. With to.
DOCILITY. s. {docilité, Fr. from docilitas, Lat.} Aptness to be taught ; readiness to learn. Grew.
Instances where 'docile' means neither 'teachable' nor 'tractable'
Many instances of docile over the years have applied to domesticated animals, and at times references to the docility of such animals goes beyond suggesting their obedience to suggesting a quality of peacefulness—of tameness in a sense similar to nonaggressiveness. And the continuum from peacefulness to passivity (that is, calm) is not especially long.
One instance where docile seems to mean something much closer to "submissive" or "subservient" than to "teachable" or "manageable" is Lois Beardslee, The Women's Warrior Society (2008):
We need you to be docile. So that Ogitchidaakwe, she becomes docile. Becomes the best docile she knows how. Looks around her for docile. Imitates that docile. Does docile so good she becomes a caricature of docile. White man says, "You actin' all docile like that tryin' to make fun of me? You actin' all docile like that tryin' to draw attention to yourself? Tryin' to make me look like the bad guy told you to be all docile?" And that Ogitchidaakwe, she says no sir and looks down at her feet.
Consider this note on Channel Island foxes in H.M. Menino, Darwin's Fox and My Coyote (2008):
Although they are small and so docile that Gary was able to handle them without sedation, the Island foxes had by default been the top predators on the Channel Islands ever since DDT wiped out the bald eagles.
The sense here appears to be "tame or gentle" or, in Elijah Coles's words, "easie to be handled"; but even so, one might very easily replace docile with calm without raising most readers' eyebrows.
Next consider this comment about a type of venomous snake in James Dunnigan & Albert Nofi, Dirty Little Secrets of the Vietnam War (2014):
You could encounter snakes anywhere while in the open or inside. ... In the fields you might encounter the krait. There are several species of these in Vietnam, with the largest one (five feet), the banded krait, so docile that few bites have ever been recorded. But the smaller kraits are keen on biting, and half their victims die, even if they obtain antivenom treatment.
The banded crait isn't so much manageable—soldiers weren't trying to teach the snake tricks or train it to stay out of their tents or even to handle it at all, as Gary did the foxes in the previous example—as nonaggressive. And treating the animal anthropomorphically, we might again characterize its nonagressiveness as "calm." In any event, the authors felt comfortable calling banded kraits as "docile."
Another instance where docile evidently has the sense "nonviolent" is in David Knipe, Vedic Voices: Intimate Narratives of a Living Andhra Tradition (2015):
But the seasonal rhythm always turns to its opposite, the dry period when a stream becomes so docile that cows may saunter and cowpaddle from bank to bank where hundreds of new sand islands have appeared.
Here the only coherent way to read docile is as meaning "slow-flowing and nonturbulent"—in a word, "calm."
Conclusion
Writers and speakers have used docile in the sense of "manageable, tame, or easy to handle" for a long time; but instances in which they have used the word unambiguously to mean something closer to "submissive" or "nonaggressive" or "calm" are harder to find even today—and I couldn't find any such examples from earlier than about 2008. Nevertheless, I would not be at all surprised to see docile in the sense of "tame" soon make the short hop in popular understanding to docile in the sense of "calm," if indeed it has not already done so.
