I think there's no special rule for the State Department cables. The general rules are:
Executive Order 13526 establishes the mechanisms for most declassifications, within the laws passed by Congress. The originating agency assigns a declassification date, by default 10 years. After 25 years, declassification review is automatic with nine narrow exceptions that allow information to remain as classified. At 50 years, there are two exceptions, and classifications beyond 75 years require special permission. Because of changes in policy and circumstances, agencies are expected to actively review documents that have been classified for fewer than 25 years. They must also respond to Mandatory Declassification Review and Freedom of Information Act requests. The National Archives and Records Administration houses the National Declassification Center to coordinate reviews and Information Security Oversight Office to promulgate rules and enforce quality measures across all agencies.
So basically everything from the 1930s should be declassified. Accessing these materials may required a trip to the National Archives though.
For example, news from 2017:
Prominent Papuans pleaded for the U.S. to give them money and arms in the mid-1960s to fight Indonesia’s colonization of their vast remote territory, according to recently declassified American files that show the birth of an independence struggle that endures half a century later. [...]
The files are among the thousands of pages of cables between the State Department and the U.S. Embassy in Jakarta from the 1960s that were declassified earlier this year. The 37 boxes of telegrams are stored at the National Archives and Records Administration in Maryland and researchers are working on making them available online.
N.B. the same set of cables showed the extent of US knowledge of the killings committed by the Sukarno regime at the time.