See, we can't speculate who is the ninth avatar and who is not. We can only check what the scriptures say about it. Already there have been two-three questions regarding this on the site. So I am answering it briefly.
Scriptures describe incarnations of Vishnu as infinite. And not all incarnations happen in our material plane. Those incarnations in which the Lord descends to this material plane of existence are known as avatars. And even among those, only ten are prominent and most important as per the scriptures. Mastya, Kurma, Varaha all are avatars because the Lord assumed a seemingly material form for the sake of the earth and gods.
Now it's true that the ninth avatar is somewhat controversial because it portrays Buddha as an avatar of Vishnu. Why? Because Vishnu is a Vedic god and Buddha spread a non-Vedic tenet telling everyone to reject the Vedas and yajnas. Some say due to Buddha's influence as a teacher who affected so may people around the world, He was accepted as an avatar of Vishnu. We can't say whether it's true or not, but in the scriptures Buddha has been mentioned as an avatar of Vishnu. We can't change that. Otherwise Gaudiya Vaishnavas who accept Chaitanya Mahaprabhu as an incarnation of Krishna would certainly list Him in the ten avataras. So also many other sects and cults would replace the ninth avatar with their worshiped deity or preceptor. But then, they would not be able to provide scriptural proofs to back up their claims. It's because most of the scriptures mention Buddha as the ninth avatar and some also mention Balarama as the ninth avatar. If we don't go by the book, then it's all just a matter of personal preference whom we accept as the ninth avatar, after all, all avatars are nothing but Vishnu Himself.
For scriptural references regarding the ten avatars, please see this answer.