I was just wanting day and month
King Diamond: “The 7th Day of July 1777”
Also, do song titles count? Rick Springfield has “April 24, 1981” but the date’s not mentioned in the lyrics.
From the album Finn by the Finn Brothers (but pretty much just a Neil Finn effort) The Last Day of June.
Neil Finn is possibly better known for his work in **Crowded House **and both brothers for Split Enz.
TCMF-2L
“You know I remember the 23rd of November” - “Hijack” (Jefferson Starship)
Honorary mention for the Jefferson Airplane’s “Re-Joyce” which is about James Joyce’s novel “Ulysses” that takes place entirely on June 16, 1904 (though the song doesn’t ID the date.)
“Karma’s Payment” - Modest Mouse
uh-oh down low
I am not who I want to be
I probably will not ever be
I drove my car on June 14th
I want to be with you, be with you…on New Year’s Day (U2)
And because it’s a boring day at the office and I have nothing else to do:
JANUARY
I want to be with you, be with you…on New Year’s Day (U2)
MARCH
In the morning in the winter shade / On the 1st of March on the holiday
If I am guilty so are you, it was March 4th, 1982
APRIL
Early morning, April 4th, shot rang out in the Memphis sky.
April 24, 1981
MAY
It’s the first of May, first of May, outdoor fucking starts today…
Night of the 4th of May…
Born on the 21st of May.
Everyone would gather on the 24th of May, sitting in the sand to watch the fireworks display.
JUNE
It was the 3rd of June…
It was the dark of the moon on the sixth of June
I drove my car on June 14th
The Last Day of June 1934
It was June, of 1983…
The 31st of June (not a real date however)
JULY
Saturday in the park…I think it was the 4th of July…
"I can remember the fourth of July…
The 7th Day of July 1777
SEPTEMBER
It was the 3rd of September.
Do you remember / The 21st night of September?
NOVEMBER
Remember the fifth of November
The Last Day of June
DECEMBER
The first of December was covered with snow…
Late December, back in '63…
NEVER
The 12th of Never
Shite! I realized I made a mistake there. Since I missed the edit window…
JANUARY
I want to be with you, be with you…on New Year’s Day (U2)
MARCH
In the morning in the winter shade / On the 1st of March on the holiday
If I am guilty so are you, it was March 4th, 1982
APRIL
Early morning, April 4th, shot rang out in the Memphis sky.
April 24, 1981
MAY
It’s the first of May, first of May, outdoor fucking starts today…
Night of the 4th of May…
Born on the 21st of May.
Everyone would gather on the 24th of May, sitting in the sand to watch the fireworks display.
JUNE
It was the 3rd of June…
It was the dark of the moon on the sixth of June
I drove my car on June 14th
The Last Day of June 1934
It was June, of 1983…
The 31st of June (not a real date however)
JULY
Saturday in the park…I think it was the 4th of July…
"I can remember the fourth of July…
The 7th Day of July 1777
SEPTEMBER
It was the 3rd of September.
Do you remember / The 21st night of September?
NOVEMBER
Remember the fifth of November
You Know I remember the 23rd of November
DECEMBER
The first of December was covered with snow…
Late December, back in '63…
NEVER
The 12th of Never
Sublime has lyrics “April 26th, 1992”, in a song strangely titled April 29, 1992.
What happened to those three days? 
“Marie Provost did not look her best
The day the cops bust into her lonely nest
In the cheap hotel up on Hollywood West
July 29”
“Marie Provost”, Pure Pop For Now People, Nick Lowe
“It was the third of June…
…
It was the fourth of June”
Desiree, Neil Diamond
“It’s the tenth of January…”
Darkest Hour, Arlo Guthrie [which came up on my iPod for my first hearing of it ever, on January 10! Plus my mom died just after midnight 1/10/10]
“But you turned to no one / But a bullet and a gun
And the bang blended in with the day
…
Then the fourth of July is a good day to die
They’ll celebrate each year, your independence from here”
**
Fourth of July, Pete Drogue**
Paul Kelly - How to Make Gravy
Hello Dan, it’s Joe here
I hope you’re keeping well
Its the 21st of December
now they’re ringing the last bell
if I get good behaviour
I’ll be out of here by July
Won’t you kiss my kids on Christmas day
And I see forests/It’s the 25th of December/And my old man plays the piano for Christmas. —25th December by Everything But The Girl
“Was the tenth day of February when he said
He just met Valentine’s Day in Juarez”
-The Ike Reilly Assassination, “Valentine’s Day In Juarez”
“Let’s travel back in time,
2/12/99 at the stroke of midnight
Holding you tight, your body and mine, in February”
-The Starting Line, “Leaving”
“First day of August
The last rain was in May
When the rainmaker came to Kansas
In the middle of a dusty day”
-Harry Nilsson, “Rainmaker”
“She caught my eye on October 9th,
22 days before Halloween,
How did I know she’d be my evil queen”
-Good Charlotte, “Walk By”
The Lady’s got Potentialfrom Evita.
"It was January 22nd 1944. "
Elton John had an album titled 11/17/70 (17/11/70 in the UK), though no song lyrics about the date.