My guess 1/2 - ours has the 1/2" lug nuts. Mine have 1/2-20 on the side of the lug nut. A 9/16 would probably have 9/16-18 on the side.
Take a look at this page for pictures of lug nuts.
https://www.etrailer.com/s.aspx?qry=lug+nuts
The lug nuts do loosen a little on the first trip - 50 to 100 miles.