Henry of Poitou, Abbot of Cluny 

 According to the historian Alfred Richard, author of Histoire des comtes de Poitou, Henry's identification as a son of William IX was an error. Henry first appears as a prior of Cluny in an 1100 charter, making him far older than William's children. In addition, Henry is not named among the children of William IX in the chronicle of Saint-Maixent; I can't imagine such a prominent individual would've been overlooked had he in fact been a son of William. 

 To my knowledge, no early or near-contemporary source mentions any illegitimate children for William IX. That doesn't mean that he didn't have any, it just means none were recognized, or important enough to be mentioned. Henry's mother certainly wasn't William's most famous mistress, Dangereuse, who only took up with William around 1113. Raoul de Faye, who is sometimes listed as a son of Dangereuse and William, was actually Dangereuse's son by her husband. She and William don't seem to have had any children together. 

 Henry of Poitou was evidently of high birth, as mentioned by the Anglo-Saxon Chronicle and the Laud Chronicle. But he doesn't seem to have been a son of William IX; indeed, he was closer to William's age in all probability.