There were few changes for the 1959 model year Corvette; perhaps GM figured people still needed time to absorb the 1958 styling.
The styling was toned down a notch as the faux louvres disappeared from the hood (above) and (below) the trunk "spears" were gone. Years later the change is considered to be the correct move as 1959 / 1960 Corvettes genrally get higher prices than the 1958 model.
Above: Brochure illustration shows the dashboard which was completely revised in 1958. 1959 additions included a storage bin below the passenger grab handle. A "Corvette" script was added to the anodized aluminum area behind the grab bar.

Corvette C1 5,500 and 6,500 RPM tachometers. Above: The base 230 HP and 245 HP and 250 HP fuel injected optional engines (basically those with hydraulic lifters) had a 5,500 RPM redline. Below: The 270 HP and 290 HP fuel injected motors, which used solid lifters, had a 6,500 RPM redline.
Above: T-handle manual shifter and below: Brochure description. To engage reverse, the handle had to be pulled up; this prevented accidental reverse selection. The feature was new for 1959 four speeds and would continue through the C2 and into the C3 Corvette generations.
Interior, in person (above) and per the brochure (below). 1959 was the first year a black interior was available in the Corvette. The door panel was redesigned for more elbow room. Note the transverse (door panel to door panel) seat stitching. This is one of the ways to differentiate the 1959 and 1960 Corvettes; another is that 1960 Corvettes featured body colored wheels. The '60 vettes had front to back seat stitching.
1960 Corvette
1959 Corvette Options