The Jamaican National Team was a participant in the 2014 Quidditch World Cup tournament in Argentina. They lost to the USA 240 to 230 after their Keeper, Kquewanda Bailey, fell due to a delayed illness caused by a team mascot at the opening ceremony of the tournament. While she was unconscious, Seeker Shanice Higgins was beaten to the Snitch by her US rival (Pm).
Although Jamaica fielded a Quidditch World Cup team in the 2014 tournament, no Quidditch teams or evidence of any other wizarding sports is noted on their Wikipedia entry (Wikipedia: Jamaica).
From the Web
Screenshots of the Daily Prophet's coverage of the 2014 Quidditch World Cup: http://imgur.com/a/AXutv