The original tires on a 1960 Cadillac were 8.20 x 15 4-ply, with 2-1/4" whitewall. Several different brands were used -- I have had them with U.S. Royal and B.F. Goodrich.
Most 1959 and 1960 Cadillacs that you see today have whitewalls that are wider than the originals.
Just as an aside, 1961 was the last year that GM cars used "wide whitewalls" -- that is, whitewalls that came all the way to the inside edge of the tire. The only exceptions were the Chevrolet Impala SS and the Corvair Monza, which used narrow stripe whitewalls in 1961, a trend that would spread to all GM cars by 1962.