a person who loves drinking alcohol
飲兵衛 (のんべえ) and also 飲助 (のみすけ) mean “people who love drinking”. Both words presumably originate from real person’s names, as 兵衛（べえ）and 助 (すけ) used to be commonly used in people’s names, such as 権兵衛 (ごんべえ) and 愛之助 (あいのすけ). While 兵衛 now sounds old-fashioned and is not very popular, 助 is still used in some names, such as 慎之助 (しんのすけ).
Because he loves drinking, he will be happy if you bring him Japanese sake.