The Booker T and The MG's ' Abbey Road ' album. I think it was released in early '70 so recorded in late '69.
I suppose this thread wouldn't be complete without this: Herb Alpert & The Tijuana Brass / All My Loving
For me the very best of that era are these: Joe Cocker - "With A Little Help From My Friends" Yes - "Every Little Thing" Carpenters - "Ticket To Ride" Rolling Stones - "I Wanna Be Your Man" Nilsson - "You Can't Do That" + Crosby, Stills & Nash - "Blackbird" (recorded in 1969 but not released until 1991)
Geez, I love that. A big favourite for me is The Sunshine Company doing 'I Need You'. https://www.youtube.com/watch?v=avANncr8GyU
One more from the Carpenters. Rich and Karen on all the vocals, Rich on the keys and Karen & Hal Blaine on drums. From their 1970 Close To You lp. This is the original audio but it is always fun seeing Karen pounding her kit.
Joe Meek produces a Beatles cover -- "All My Loving" by the Dowlands, released in the U.S. as Tollie 9002:
Didn't see anyone list this one. Goes back to '68 -- for those who like heavy psychedelic -- Help - Deep Purple (1968)
Shirley Scott w/Stanley Turrentine, like the Lonnie Mack above this wasn't issued at the time, Turrentine also did a version of this on his own around the same time but it wasn't issued initially either.