Syria won the 1974 Quidditch World Cup after beating a team from Madagascar in the final match. This Quidditch World Cup tournament is mostly remembered for the mass rule-breaking known as “Royston Idlewind and the Dissimulators” (Pm).
Although they had a Quidditch World Cup win in 1974, no Quidditch or any other wizard sports team is listed on Syria's Wikipedia entry (Wikipedia).
From the Web
Writing by J.K. Rowling on Pottermore:
Pottermore enhanced reading experience: Quidditch World Cup
Screenshots of the original Daily Prophet coverage of the 2014 Quidditch World Cup on Pottermore: Imgur archive
Harry Potter Wiki: Syrian National Quidditch Team