Songs like “Good Morning, Good Morning” by the Beatles or “Tuesday Afternoon” by the Moody Blues wouldn’t count, for example.
Here’s a start:
“11:59” - Blondie
“5:15” - The Who
about a zillion songs with “midnight”
What else?
“25 or 6 to 4”–Chicago
8:16am by 311
Wednesday Morning, 3 AM by Simon and Garfunkel
‘9 to 5’ - Dolly Parton
Nine to Five by the Kinks
‘In the wee small hours of the morning’ - Frank Sinatra
It’s three o’clock in the morning,
We’ve danced the whole night through!
And daylight soon will be dawning,
Just one more waltz with you . . .
9 to 5(Morning Train) - Sheena Easton(Different than the Dolly Parton song)
Hello!!!
Rock Around the Clock as performed by Bill Haley and the Comets
One, two, three o’clock, four o’clock, rock,
Five, six, seven o’clock, eight o’clock, rock,
Nine, ten, eleven o’clock, twelve o’clock, rock,
We’re gonna rock around the clock tonight.
etc.
Five O’Clock World – the version I know is a cover by country singer Hal Ketcham. I’m not sure who originally recorded it.
12:51 by the Strokes
Hello! There’s no specific time mentioned in the TITLE.
But thanks for playing. 
Night Ranger had Four In the Morning.
Matchbox Twenty’s “3 am”
Count Basie’s “One o’ Clock Jump”
ATB’s “Nine O’ Clock (Til I Come)”
John Cage’s “4:33” (which is a long shot and a technicality, but hey!)
In addition, AllMusic returns a huge list of songs with titles that match “half past” and a slightly shorter list of “quarter til” songs.
“One O’clock Jump”, Count Basie
“Two For The Show”, Kansas
“Three Coins in The Fountain”, Jule Styne/Sammy Cahn, sung by the Four Aces
“One Dyin’ and A Buryin’”, Roger Miller
“The Twelve Days of Christmas”, various
“Six Days On The Road”, Dave Dudley
“The Magnificent Seven” (movie theme), Elmer Bernstein
“15 Beers Ago”, Sheb Wooley
“500 Miles”, Bobby Bare; Peter, Paul & Mary
And that’s just off the top of my head.
The Vogues.
“Six O’Clock” - Lovin’ Spoonful
“Six O’Clock” - Ringo Starr
“Quarter to Three” - Gary U.S. Bonds
How could I forget?
“Route 66”, Nat King Cole (and sung later by the Stones)
“77 Sunset Strip”, Mack David and Jerry Livingston
Actually, this is the only one of your list that satisfies the OP.
Chefguy, 1 out of 11 ain’t bad!