The Greek and Hebrew phrases that are often translated as “birds of the air” in English “refer to the undomesticated song birds or wild birds, to be distinguished in a number of languages from domesticated fowl. In Tzeltal these former are ‘field birds’.” (source: Bratcher / Nida)
Q’anjob’al also uses an established term for non-domesticated birds. Newberry and Kittie Cox (in The Bible Translator 1950, p. 91ff. ) explain: “Qʼanjobʼal has two distinct terms, one to identify domesticated birds and the other non-domesticated birds. The additional descriptive phrase ‘of the air’ seemed entirely misleading, for Qʼanjobʼal speakers had never heard of such creatures. Actually, of course, all that was necessary was the term for non-domesticated birds, for that is precisely the meaning of the Biblical expression.”
In Elhomwe they are just translated as “birds” or “birds of the bush” (i.e., wild birds) to “not give the impression that these are special type of birds.” (Source: project-specific translation notes in Paratext)
See also birds of the air / fish of the sea and birds or four-footed animals or reptiles.