People get Ready, Curtis Mayfield
Sorry 'bout that… thought the OP read 64-74, not 69-74. PGR was written in 1964.
Kristopherson’s “The Law is for Protection of the People”:
So thank your lucky stars you got protection.
Walk the line and never mind the cost.
Don’t wonder who those lawmen were protecting
When they nailed the Savior to the cross.
Cause the law is for protection of the people.
Rules are rules and any fool can see
We don’t need no riddle speaking prophets
Scaring decent folk like you and me. No sireeeee.
God Gave Rock and Roll to You - Argent
“Rock and Roll Heaven” - The Righteous Brothers (sorta)
“Signs” - Five Man Electrical Band (sorta)
Perhaps Morning has Broken by the former Cat Stevens? I’m not religious in the slightest, but I like Rick Wakeman’s piano on that song a lot…
Also, obscurely, maybe As sure as Eggs is Eggs, which is the finale to the Genesis suite Supper’s Ready from Foxtrot.
Does My God by Jethro Tull count? Probably not.
Spirit did Jewish, a jazz-rock version of a prayer in Hebrew.
“I can feel him in the morning” by Grand Funk
I think it counts, and that George’s Sweet Lord could be equated with “God” for the purposes of this thread. Particularly since he sings, “They call you Christ, Vishnu, Buddha, Jehovah, Our Lord / You are Govinda, Bismillah, Creator of All” in a later song (“Life Itself”).
Also from George: “Awaiting On You All,” and probably several others.
And if you stretch the time interval a little, you can add “Have a Talk With God.”
The 1969-1974 time period does encompass the beginnings of the Christian Rock genre, with early works by artists such as Larry Norman and Petra.
Ansd of course there was Janis Joplin’s “prayerful” song “Mercedes Benz”. 
• “The Lord’s Prayer” by rockin’ Sister Janet Mead, which went to #4 on Billboard’s pop singles charts in 1973. You bet we sang it at guitar masses in my parochial school.
• Paul Simon’s “Loves Me Like a Rock”.
• The Beatles’ “Let It Be”.
• Cat Stevens’ “Morning Has Broken”. Another favorite at guitar mass.
• Donovan’s song score for the movie Brother Sun, Sister Moon.
Just had to post a photo of Sister Janet Mead. Swing out, sister!
I loved that song & was racking my brain to remember the Sister’s name! Thanks!
Not quite in that time frame, but Jeff Beck and Rod Stewart did an awesome version of “People Get Ready”.
Also a little later, Don Henley recorded a wonderful version of “The Unclouded Day” on his first solo album, “I Can’t Stand Still”.
Did Dylan’s Christian phase start by 1974? “Serve Somebody” might qualify…
Correction. This song was by Pete Seeger and covered by the Byrds.