Hey, good thread. I’m surprised how many of these are hitting me with a blinding flash of recognition and a few lines playing softly in my head. “One More Saturday Night”: The best Nuclear Holocaust Dance Party song. 
Day By Day - I think it was off Jesus Christ, Superstar. Oh, dear Lord, three things I pray…
Sweet Tuesday Morning - Badfinger
Day Tripper
Eight Days a Week - Beatles
No, Godspell.
New Year’s Day – U2
Come Saturday Morning – The Sandpipers
Black Friday – Steely Dan
Groovy Tuesday- The Smithereens
Ironing Tuesdays- The Posies
Going with the “day” thing:
Any Day Now–Ronnie Milsap (though I think it might have been a cover)
Both Johnny Cash and Kris Kristofferson are associated with the song. Read more here.