From 笑(わら)い (warai, 連(れん)用(よう)形(けい) (ren'yōkei, “stem or continuative form”) of the verb 笑(わら)う (warau)) + 話(はなし) (hanashi). The hanashi changes to banashi as an instance of rendaku (連(れん)濁(だく)).
わらいばなし • (waraibanashi) ←わらひばなし (warafibanasi)?