"part of a newspaper's staff that works during the day," by 1942, American English, from day (n.) + side (n.).
Entries linking to dayside
day n.
Old English dæg "period during which the sun is above the horizon," also "lifetime, definite time of existence," from Proto-Germanic *dages- "day" (source also of Old Saxon, Middle Dutch, Dutch dag, Old Frisian di, dei, Old High German tag, German Tag, Old Norse dagr, Gothic dags), according to Watkins, from PIE root *agh- "a day." He adds that the Germanic initial d- is "of obscure origin." But Boutkan says it is from PIE root *dhegh- "to burn" (see fever). Not considered to be related to Latin dies (which is from PIE root *dyeu- "to shine").
Meaning originally, in English, "the daylight hours;" it expanded to mean "the 24-hour period" in late Anglo-Saxon times. The day formerly began at sunset, hence Old English Wodnesniht was what we would call "Tuesday night." Names of the weekdays were not regularly capitalized in English until 17c.
From late 12c. as "a time period as distinguished from other time periods." Day-by-day "daily" is from late 14c.; all day "all the time" is from late 14c. Day off "day away from work" is attested from 1883; day-tripper first recorded 1897. The days in nowadays, etc. is a relic of the Old English and Middle English use of the adverbial genitive.
All in a day's work "something unusual taken as routine" is by 1820. The nostalgic those were the days is attested by 1907. That'll be the day, expressing mild doubt following some boast or claim, is by 1941. To call it a day "stop working" is by 1919; earlier call it a half-day (1838). One of these days "at some day in the near future" is from late 15c. One of those days "a day of misfortune" is by 1936.
side n.
Old English side "flanks of a person, the long part or aspect of anything," from Proto-Germanic *sīdō (source also of Old Saxon sida, Old Norse siða, "flank; side (of meat); coast," Danish side, Swedish sida, Middle Dutch side, Dutch zidje, Old High German sita, German Seite), from adjective *sithas "long" (source of Old English sid "long, broad, spacious," Old Norse siðr "long, hanging down"), from PIE root *se- "long; late" (see soiree).
The "long part of anything" sense is preserved hillside, it also was in 16c.-17c. side-coat "long coat." From 14c. as "lateral half of the body of a slaughtered animal." In reference to bacon, it indicates position relative to the ribs. The meaning "a region, district" is from c. 1400, as in South Side, countryside.
The figurative sense of "position or attitude of a person or set of persons in relation to another" (as in choose sides, side of the story) is recorded by mid-13c. As "an aspect" of anything immaterial (the bright side, etc.), by mid-15c.
The meaning "one of the parties in a transaction" is from late 14c.. The sense of "one of the parties in a sporting contest or game" is from 1690s. The meaning "music on one side of a phonograph record" is attested by 1936. As short for side-dish, by 1848.
The phrase side by side "close together and abreast, placed with sides near together" is recorded from c. 1200. Colloquial on the side "in addition," especially "unacknowledged," with connotations of "illicit, shady," is by 1893.