We don't have synonyms for barbeques yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are barbecue, barbecued and barbeque.
(v) :
(sometimes proscribed) Alternative spelling of barbecue. [(transitive, intransitive) To cook food on a barbecue; to smoke food over indirect heat from high-smoke fuels.]
(n) :
(sometimes proscribed) Alternative spelling of barbecue (“apparatus for grilling; cookout (event); meat cooked by barbecuing”). [A fireplace or pit for grilling food, typically used outdoors and traditionally employing hot charcoal as the heating medium.]
(v) :
(sometimes proscribed) Alternative spelling of barbecue. [(transitive, intransitive) To cook food on a barbecue; to smoke food over indirect heat from high-smoke fuels.]
(n) :
(sometimes proscribed) Alternative spelling of barbecue (“apparatus for grilling; cookout (event); meat cooked by barbecuing”). [A fireplace or pit for grilling food, typically used outdoors and traditionally employing hot charcoal as the heating medium.]