This is a pretty difficult question to answer because name spelling isn't really orthographic, neither historically nor today.
But looking at the full data from the SSA, we see the spelling
Haley from 1890 on, albeit rare. It was eclipsed by
Hayley only in 1963, got the lead back in 1972, to loose it to
Hailey in 2001. I have not summed up the number, but I'm pretty confident that the total number of
Haley's born the USA still surpasses any other particular spelling. So, at least for the USA, I would see
Haley as the primary spelling.