I couldn't stand the character (Kay), either, but Keaton must've played the role just as Coppola wanted her to. This site claims Mia Farrow, Blythe Danner, and Michelle Phillips (of the Mamas and Pappas) also were considered for the role.
I agree with that 100% She played the part exactly as they wanted her to. I still hate watching all the parts of those movies with the whiny, rather stupid Kay character in them. That I got that kind of repellent reaction is probably just what Coppola and Mario Puzo wanted us to think about Kay. I read the book before I watched the Godfather and I don’t remember the Kay character being so hard to stand though. I think Diane Keaton in some ways brought that out in the movie.