1892: “Big Sam left Seattle, in the year of '92…”, “North To Alaska”, Johnny Horton
Where the river is windin, big nuggets they’re findin’ -
North! To Alaska!, They go north, the rush is on!
1899 “In 18 hundred and 99, when everybody sang Auld Lang Syne . . .” Twentieth Century’s Almost Over, Steve Goodman
The zero years are a challenge, because they don’t rhyme well. Anyone got anything for 1960, 1970, 1980?
I already mentioned this one in the “days of the year” thread, but it works here too:
1990. “On May 1, 1990, something changed inside me” - May 1, 1990 by Adrian Belew
1980. “They’ll be building it up in the air, ever since 1980” - Hijack by Paul Kantner
(Also mentions 1990, but Thudlow has that one covered.)
1965. “Demon-warp is coming alive in 1965” Thunder Kiss '65 by White Zombie
1972. “Don’t leave your torch behind, a power cut ahead, 1972, you know.” - Late Night, Maudlin Street by Morrissey
1958- “Born in a mining town in '58,when black and white TV was up to date”, Born in '58, by Bruce Dickinson
1945- “I left Kentucky back in '45 and went to Detroit working on an assembly line”, One Piece at a Time, by Johnny Cash
1844–“In 1844, the Democrats were split”, James K. Polk, They Might Be Giants
1990–“It’s a brand new record for 1990”, Flood, by They Might Be Giants
1967. “1967, Colt .45, holding back the vampires, keeping me alive.” - Coffee by Aesop Rock ft. John Darnielle
Hmmm. Well, the thread title asks us to “name a song that mentions a specific year”, and there are song lyrics I can think of that mention events from years such that you could date them precisely, but do not actually say the year by number. Do those count?
If so,
1970 - “This summer I hear the drummin’, four dead in Ohio” - “Ohio” by Crosby, Stills, Nash & Young [referring to the Kent State shootings of May 4, 1970]
If that’s allowed, well there are lots of things to glean from 1949-1989 from Billy Joel’s “We Didn’t Start The Fire” 
and -
1968 - “Early morning, April 4 - a shot rings out in the Memphis sky”, “Pride (In The Name of Love)”, by U2 [referring to the assassination of Martin Luther King, Jr. on April 4, 1968] (lyrical nitpick: it was 6:01pm when he was shot, not in the morning)
1969 - “I’ve been known to the do the impossible, like Broadway Joe”, “Scenario” by A Tribe Called Quest [referring to Joe Namath leading the Jets to victory in Super Bowl III on January 12, 1969]
1982: “And now you find yourself in '82.” - The Heat of the Moment by Asia.
1986: “And after 1986, what else could be new?” - Modern Woman by Billy Joel.
1957: “I get off on '57 Chevys; I get off on screaming guitar.” “I’ve Got A Rock ‘n’ Roll Heart”, Eric Clapton
1960: "Out past the cornfields where the woods got heavy/ Out in the back seat of my '60 Chevy " “Night Moves”, Bob Seger
1962: “Started humming a song from 1962”, also “Night Moves” by Bob Seger
1964 - “Back ’ 64, before you were born…”, “Back in '64” by the Rutles (from their film and album, “All You Need Is Cash” ;))
- Back in '64, before you were born,
No one had time for pouring scorn
On dreams of love and peace,
And no-one was obese,
Only tight trousers were worn…*
“In May of 1941, the war had just begun. . . .” “Sink the Bismark” by Johnny Horton.
Leonard Cohen - ‘It seems so long ago Nancy’
“She never said she’d wait for us
although she was alone,
I think she fell in love for us
in nineteen sixty one,
in nineteen sixty one.”
Also… not a recorded song, but after going twenty three years without a win at Old Trafford (Manchester Utd.'s ground), Tottenham supporters sang “We’re gonna have a party like it’s 1989”
1939. “In the year of '39 assembled here the volunteers” - '39 by Queen
4 B.C. “Israel in 4 B.C. had no mass communication” - Superstar by Murray Head
Hey all, please try to keep to the following format:
YEAR. “Song lyric that mentions that year.” Song Title by Artist.
It makes it a lot easier to compile the master list.
Thanks!
mmm
ETA:
Good one, Biffy!
1969. “Sixty-nine, was cheapo wine, have a good time, what’s your sign,” - The Saturday Gigs by Mott the Hoople. The song also goes on to mention '70, '71, '72, '73, and '74.)
1954. “The year was 1954”- The Late Great Johnny Ace by Paul Simon.
1964. “*It was 1964
*”-The Late Great Johnny Ace by Paul Simon.
1836. "Back in 1836, Houston said to Travis:- Ballad of the Alamo by Marty Robbins.
1956 (and 1957). “Said welcome to the spirit of 1956, Patient in the bushes next to '57” - Roadrunner by Jonathan Richman and The Modern Lovers.