@Bump111: You're correct!The individual with the distinction of living for the shortest time after appearing on a US commemorative coin is: Joseph Taylor Robinson; he died of heart failure about six months after the coin with his portrait was released.
Here's a quick comparison summary of the four candidates:
1. Alabama Statehood Centennial / Thomas Kilby: Coin released in October 1921, Kilby died on October 22, 1943 - approximately 22 years later. (4th place)
2. American Independence Sesquicentennial / Calvin Coolidge: Coin released in June 1926, Coolidge died on January 5, 1933 - approximately 7-1/2 years later. (2nd Place)
3. Arkansas Statehood Centennial / Joseph Robinson: Coin was struck and released in January 1937 (the "1936" seen on the coin was mandated by its authorizing legislation), Robinson, called the "fightingest" man in the U.S. Senate, died unexpectedly of heart failure on July 14, 1937 - approximately six months later. He had spent nearly 34 years serving Arkansas in various positions.
At the time of his death, Robinson, a Democrat, was the Senate Majority Leader; he had previously served as the Senate Minority Leader. Robinson was first elected to the Senate (by the Arkansas state legislature vs. public election) to replace the recently-deceased Jefferson Davis, beginning his service on March 10, 1913. He had briefly served as the Governor of Arkansas (January 16, 1913 to March 8, 1913), but resigned from the position to become the US Senator from Arkansas. Prior to being elected governor, Robinson was a member of the US House of Representatives, beginning service for Arkansas on March 4, 1903; he resigned his position on January 14, 1913 to become governor.
4. Lynchburg, VA Sesquicentennial / Carter Glass: Coin released in September 1936, Glass died on May 28, 1946 - approximately 9-2/3 years later. (3rd Place)
1936 Arkansas Statehood Centennial - Robinson Type

Fourth Place never looked so good!
I've posted about all of these coins before, you can read about them via the links at:
Read More: Commems Collection.
For a discussion of living people on US commemorative coins (classic and modern), check out:
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Alive and Well (At the Time!)