There is an ongoing controversy among scholars and a section of devotees as to whether Buddha is an avatar of Lord Vishnu. Sri Aurobindo Ghosh shares his thoughts on Buddha as an avatar of Vishnu.
As to whether one accepts Buddha as an Avatar or prefers to put others in his place (in some lists Balaram replaces Buddha), is a matter of individual feeling. The Buddhist Jatakas are legends about the past incarnations of the Buddha, often with a teaching implied in them, and are not a part of the Hindu system.
To the Buddhists Buddha was not an Avatar at all, he was the soul climbing up the ladder of spiritual evolution till it reached the final stage of emancipation – although Hindu influence did make Buddhism develop the idea of an eternal Buddha above, that was not a universal or fundamental Buddhistic idea.
Whether the Divine in manifesting his Avatarhood could choose to follow the line of evolution from the lowest scale, manifesting on each scale as a Vibhuti is a question again to which the answer is not inevitably in the negative. If we accept the evolutionary idea, such a thing may have its place.
If Buddha taught something different from Krishna , that does not prevent his advent from being necessary in the spiritual evolution. The only question is whether the attempt to scale the heights of an absolute Nirvana through negation of cosmic existence was a necessary step or not, having a view to the fact that one can make the attempt to reach the Highest on the ‘neti neti’ as well as the ‘iti iti’ line.
He [Buddha] affirmed practically something unknowable that was Permanent and Unmanifested. Adwaita does the same.
Buddha never said he was an Avatar of a Personal God but that he was the Buddha. It is the Hindus who made him an Avatar. If Buddha had looked upon himself as an Avatar at all, it would have been as an Avatar of the impersonal Truth.
I don't know that historically there could have been any other Buddha. It is the Vaishnava Puranas, I think, that settled the list of Avatars, for they are all Avatars of Vishnu according to the Purana. The final acceptance by all may have come later than Shankara, after the Buddhist-Brahminic controversy had ceased to be an actuality. For some time there was a tendency to substitute Balarama's name for Buddha's or to say that Buddha was an Avatar of Vishnu, but that he came to mislead the Asuras. He is evidently aimed at in the story of Mayamoha in the Vishnu Purana.
If a Divine Consciousness and Force descended and through the personality we call Buddha did a great work for the world, then Buddha can be called an Avatar – the tapasya and arriving at knowledge are only an incident of the manifestation.
If on the other hand Buddha was only a human being like many others who arrived at some knowledge and preached it, then he was not an Avatar – for of that kind there have been thousands and they cannot be all Avatars.
Sri Aurobindo
(Source: excerpted from Letters on Yoga, Part I, Vol 22; The Purpose of Avatarhood, page number 403 to 405.)