George Smathers is sometimes talked about as an alt-history VP for JFK due to his personal friendship with the President. As President, Smathers would probably have opposed the Civil Rights legislation that LBJ championed, but been just as bad on Vietnam.
I honestly do not know why the belief that JFK could have chosen Smathers as his running mate (either in 1960 or if it seemed necessary to drop LBJ from the ticket in 1964) is so widespread here. (FWIW, in all the books I have read concerning JFK's potential running mates, Smathers is never even mentioned as a possibility.) Maybe it stems from the fact that JFK and Smathers were friends. But presidential candidates have lots of friends whom they know it would be foolish to put on the national ticket. And in any event, according to an interview Smathers gave decades later, the JFK-Smathers friendship was strained by Smathers' decision to run as a favorite son presidential candidate from Florida in 1960.
https://books.google.com/books?id=CeldDwAAQBAJ&pg=PA151 (That candidacy made it substantially less likely that JFK would win on the first ballot.)
Putting someone who had signed the Southern Manifesto on the national ticket would be incredibly risky in close northern and border states like Illinois, Missouri, New Jersey, Pennsylvania, and Michigan, where the African American vote could make the difference. LBJ was the ideal running mate because he had southern support yet had not signed the Manifesto--indeed the southerners didn't
want him to sign it because they knew that would destroy his chances of winning the Democratic presidential nomination. LBJ even got the support of some black political leaders like Adam Clayton Powell, Jr., something Smathers could never have gotten. And if LBJ declined and JFK was still insistent on a southerner, there were others less toxic to northern liberals and African Americans than Smathers--Albert Gore, Sr. of TN for example.
Florida was still a rather small southern state in 1960--it had only 10 electoral votes, no more than KY or LA. But in the very unlikely event JFK wanted to put a Floridian on the ticket, LeRoy Collins would be at least marginally more plausible.
https://en.wikipedia.org/wiki/LeRoy_Collins
Also, as I wrote here a couple of years ago, "There is also the obvious fact that seems to be ignored here that LBJ, Symington, Scoop Jackson, Humphrey and the other people mentioned for the vice-presidency were all men of stature, men who could be taken seriously as president--as could Henry Cabot Lodge on the Republican side. One reason that Smathers was never seriously mentioned is that he was an obvious lightweight who could not be taken seriously as president. That might not have changed many votes, but in as close a race as 1960 not that many votes had to be changed. Nixon's claim that JFK was a frivolous immature playboy--in contrast to the more "mature" Nixon--would only be strengthened by choosing someone solely because he was a personal friend....Smathers was a pal, no doubt. But Bebe Rebozo, another Floridian, was Nixon's pal (actually it was Smathers who got them acquainted!) and I doubt that Nixon ever considered him as a running mate."