“What time is it?”
“It’s a quarter past ‘wee’”.
While ArchiveGuy already pointed out that these songs don’t count, Route 66 was also covered by Depeche Mode.
Two Minutes to Midnight - Iron Maiden
3am Eternal by the KLF
“Four O’Clock in the Morning” - The Pogues
“10:15 Saturday Night” - The Cure
“2:10, 6:18 (Doesn’t Anybody Know My Name)” - Rod McKuen*
“3 A.M.” - Bill Anderson*
“The Little Box of Pine in the 7:29” - Marty Robbins*
“Six O’Clock Rock” - Johnny O’Keefe
*and others
It’s well known that some people post to threads without ever reading them.
Now it looks like some people post to threads without even reading the title.
All the songs on Roger Waters’ Pros and Cons of Hitchhiking:
“4:30 AM (Apparently They Were Travelling Abroad)”
“4:33 AM (Running Shoes)”
“4:37 AM (Arabs With Knives and West German Skies)”
etc.
8:15 by The Guess Who
Six O’Clock News by Kathleen Edwards, and a different
Six O’Clock News by John Prine
The entire album Days of Future Passed by The Moody Blues qualifies. The tracks are:
- The Day Begins
- Dawn: Dawn Is I a Feeling
- The Morning: Another Morning
- The Afternoon: a) Forever Afternoon (Tuesday?)
b) (Evening) Time To Get Away - Evening: a) The Sunset
b) Twilight Time - The Night: Nights in White Satin
But Does Anybody Really Know What Time It Is? 
Oh, really?
My thought, as well. 
And my contribution: “7 O’Clock News/Silent Night” by Simon & Garfunkel
Ice T had “6 n the Mornin’” and “Midnight.”
10:15 Saturday Night, the Cure.
Aw, a one-minute margin of error should be close enough. 
To contribute:
“6:00” by Dream Theater
D
11 O’Clock Tick Tock by U2.
Also, 5 O’Clock World was also covered by Julian Cope.
Here are just a few:
In the Midnight Hour - Wilson Pickett
Moanin’ at Midnight - Howlin’ Wolf
Midnight Blues - Blind Willie McTell
Midnight Rider - Allman Brothers
I also thought of From Four 'Til Late, by Robert Johnson.
4 P.M. - The Clouds
Midnight Train to Georgia - Gladys Night and the Pips (or the Indigo Girls, which is where I first heard it)