Other than 'When Angels Wept' by Eric G. Swedin, which covers the Cuban Missile Crisis, but goes down the nuclear war route, I'm not aware of any that cover anything conventional, which doesn't mean there isn't of course.
Brendan DuBois wrote the novel "Resurrection Day", which was set after the crisis in a recovering America and offers some brief glimpses of how the invasion went. I liked it, especially the hatred of Kennedy amongst the survivors, the belief amongst some that 'Kennedy lives', which provides the back story and the patronising nature of the British. You could probably pick huge holes in it here and there, but as most fiction goes, it was quite good I thought.
Obviously the main flashpoint of the fifties-sixties, besides Cuba, was the Berlin Crisis 1958 to 1962. I'm not aware of anything on that, besides an academic paper I heard of way back.
As you and I know, being of an age, the big explosion in 'what ifs' came in the 80's, with General Hackett and Harold Coyle, amongst others.