We don't have synonyms for fourball yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are football, furball and sourball.
(n) :
(golf) A match between two teams of two golfers, each playing his or her own ball throughout the round rather than alternating shots, and each hole won by the team whose individual golfer has the lowest score.
(n) :
(golf) A match between two teams of two golfers, each playing his or her own ball throughout the round rather than alternating shots, and each hole won by the team whose individual golfer has the lowest score.