Why did most airliners have black noses in the 60's and 70's?
Under the nose of modern airliners is weather radar that helps the crew to see and avoid hazardous weather conditions. This is required by FAA CFR §121.357 for transport category aircraft. The radar signal would be blocked by the aluminum that makes up the rest of the fuselage, so the radome is made of a non-metallic material, generally a fiberglass composite.

These threads discuss the topic. The last post in the first linked thread suggests that most paint needed lead to prevent fading and/or a zinc-based primer, which would interfere with the radar. Black was one color that did not require these. Modern paint has done away with these metal additives, allowing more color options without interfering with the radar.

The Museum of Flight claims that the black color is only to remind crews to not paint over the radome. Painting over it would affect the radar signals.

According to this thread, the color of the radome affects the operation of the weather radar underneath. They were painted black because it has the lowest reflectivity. Modern radars are able to deal with different colors much better.