When Adams and Jefferson were President and Vice President respectively they were in the midst of their feud and were extremely bitter towards one another. Adams and Washington also had their issues but far less so. Also Johnson and Lincoln were not so hot either. And later when Vice Presidents were selected at times to gain more political leverage or to win a key state you would have Presidents and Vice Presidents who were Luke warm towards one another. Eisenhower and Nixon being a Prime example of that.

But keep in mind that originally whoever came in second in the electoral college would become Vice President; this changed however with the 12th Amendment.

Just thought I'd give a quick answer until someone with more expertise can get more into depth about Presidential Relations.

Sources:

US Constitution

Eisenhower and Nixon: Two terms but not much endearment. Tom Feran, February 19th 2013. https://www.google.com/amp/www.cleveland.com/articles/10024525/eisenhower_and_nixon_two_terms.amp?client=safari