I’m not white, by the way; I’m half Native American and half Black. “West” was probably not the word that I should have used. What I mean is American artists or British artists who appear on the Billboard and other music charts.
Now you’re gonna upset the Canadians… 
A few more suggestions:
Bobby Bloom: Montego Bay
Eddie Grant: Electric Avenue
Billy Joel: River of Dreams
Talking Heads—Remain in Light
Byrne & Eno—My Life in the Bush of Ghosts
Canadian artists, too! I consider Canada as being part of America.
Eddie Grant is borderline. He’s already from the Caribbean but moved to England when he was young.
It’s all good - I have no problem with any of my suggestions being shot down. It’s not like I’m Canadian and just found out all my geography and history books were wrong. :D:D:D
Please step away from the shovel now 
Peter Gabriel has several songs with African influences, such as “Signal to Noise,” “Solsbury Hill,” and “In Your Eyes,” and “Biko”
Led Zeppelin’s D’yer Mak’er has strong Afro-Caribbean influences (including, at least in part, the name of the song).
Even beyond that one song, Vampire Weekend’s whole sound is heavily influenced by West African pop music anyway.
You’re right, but since posting I realized none of their music would fit fit the criteria of songs from the 50s through 90s since they were formed in 2006. 
The Police, “Every Little Thing She Does is Magic”
Genesis, “It’s No Fun (Being an Illegal Alien)”
UB40, “Red, Red Wine” (I know Neil Diamond wrote it and did it first, but…)
Any Jimmy Buffett tune using steel drums
The earliest UK punk rock incorporated ska rhythms and structures, as ska was a very conspicuous presence in London working-class neighborhoods.
Early blues songs used an African instrument called the “Diddley bow,” notably Lonnie Pitchford and the Funk Brothers. It’s kind of a one-string zither that uses a bottle as a slide. Bo Diddley has no apparent connection.
These are just the most over-the-top examples I can think of; few American songwriters since the Civil War don’t have some kind of conspicuous link to African music.
Louie Louie
Another Saturday Night
I was going to mention the Police, as well. Most of their music has a strong Afro-Caribbean influence, especially via Stewart Copeland’s drumming, but the melody lines are also often quite Jamaican influenced, see “Roxanne,” for another example with a strong reggae influence. But it doesn’t seem to fit the parameters the OP laid out in post #15, otherwise, it’d be hard not to name a pop song without some African or Afro-Caribbean influence. Even if we want to stick with more obvious influences, take something like the “Bo Diddley beat.” That’s an Afro-Cuban son clave rhythm shifted from the clave to a rhythm guitar, for instance.
Another from Elton John: Durban Deep, from his 1989 album Sleeping With the Past.