Buddha
The ninth descent is the one where the lists themselves disagree, and the disagreement is worth understanding rather than hiding. In the most widespread version, the ninth avatāra is the Buddha — the historical teacher Siddhārtha Gautama, awakened beneath the Bodhi tree, whose message of compassion (karuṇā) and non-violence (ahiṃsā) reshaped the spiritual life of Asia. But in a number of important traditions, the ninth place is held instead by Balarāma, the elder brother of Kṛṣṇa, and this variation has a long and revealing history.
Consider first the Buddha. By including the founder of a separate religion among Vishnu's descents, the Hindu tradition made a striking gesture — though not always a simple or generous one. Two quite different interpretations developed. In the more sympathetic reading, the Buddha is Vishnu come to teach compassion and turn people away from cruelty, especially from the harming of animals in sacrifice. In an older and more polemical reading found in several Purāṇas, Vishnu took the form of the Buddha to deliberately mislead the wicked into abandoning the Vedas, so that they might be marked out and the proper order preserved. Both readings coexist in the texts, and honesty requires naming both.
Now consider Balarāma. Many older and many regional lists — including strands within Vaiṣṇavism, and especially traditions that hold Kṛṣṇa to be the supreme Lord rather than a mere avatāra of Viṣṇu — place Balarāma as the ninth. The reasoning is theological: if Kṛṣṇa is God himself, then his brother Balarāma (regarded as an embodiment of the cosmic serpent Śeṣa/Ananta, Vishnu's own support) fits naturally into the divine sequence, whereas including the Buddha — founder of a rival path — sits awkwardly. The Jagannātha tradition of Puri, where Balarāma (as Balabhadra) is worshipped beside Krishna and Subhadra, reflects this strongly.
So which is "correct"? Neither, exactly. Both lists are genuinely ancient and genuinely Hindu, and the choice between them tracks deep currents — the historical effort to make sense of Buddhism, and the theology of particular Vaiṣṇava communities. A thoughtful devotee can hold the variation lightly: in one telling, the ninth face is the awakened teacher of mercy under the tree; in another, it is the strong, plough-bearing elder brother who upholds the world. The disagreement is not a flaw in the tradition but a window into how living it is.