Alochana-Buddha as the 9th. Avataar of Vishnu

From here

Buddhism is a dharmic religion. The systems of Buddhism and Hinduism must not be considered to be either contradictory to one another or completely self contained. Coomaraswamy wrote:
"The more supreficially one studies Buddhism, the more it seems to differ from Brahmanism in which it originated; the more profound our study, the more difficult it becomes to distinguish Buddhism from Brahmanism, or to say in what respects, if any, Buddhism is really unorthodox." [2]
Buddhist scholar Rahula Vipola wrote that the Buddha was trying to shed the true meaning of the Vedas. Buddha is said to be a knower of the Veda (vedajña) or of the Vedanta (vedântajña) (Sa.myutta, i. 168) and (Sutta Nipâta, 463).

Hinduism and Buddhism share many common features including Sanskrit, yoga, karma and dharma. Indians such as Ashoka the great and B.R. Ambedkar took to Buddism. India also is home to the government of Tibet in exile under Tenzin Gyatso, the 14th Dalai Lama.

In addition, Siddhartha Gautama is seen in Hinduism as the ninth avatar of Vishnu.

Buddha (meaning 'the enlightened one') appeared in the Kali Yuga (specifically as Siddhartha Gautama).

From here

The Buddha in Puranic scripture

Amongst the MahaPuranas he is mentioned as one of the ten Avataras:

The description of Buddha incorporated in ten incarnations in Puranas comes with slight difference here and there in various Puranas like,
Harivamsha (1.41),
Vishnu Purana (3.18),
Bhagavata Purana (1.3.24, 2.7,37, 11,4.23) [7],
Garuda Purana (1.1),
Agni Purana (16),
Narada Purana (2.72),
Linga Purana (2.71),
Padma Purana (3.252) etc. (Dhere Ramchandra Chintaman) [8]
Other important scriptures which mention him is an Avatar are Rishi Parashara's Brihat Parashara Hora Shastra(2:1-5/7)

During the Guptas, one of the nine gems of the court of the king, Amarasimha refers to the Buddha in the following commentary: Amarakosha-grantha (Sanskrit dictionary) list many of the names and epithets by which the Buddha is traditionally known:

sarvajnah sugato buddho dharmarajastathagatah
samastabhadro bhagavan marajillokajijjinah
shadabhijno dasabalo ’dvayavadi vinayakah
munindrah srighanah sasta munih sakyamunistu yah

All-knowing, transcendental, awakened, king of righteousness, he who has come, beneficent, all-encompassing, lord, conqueror of the god of love-mara, victorious of three worlds, he who controls his senses, protector from the six enemies, possessor of the ten powers, speaker of non-dualism, teacher, lord of the sages, embodiment of splendor and eminent saint.

sa sakyasimhah sarvarthasiddhah sauddhodanisca sah
gautamascarkabandhusca mayadevisutasca sah
teacher of the sakyas, lion of the sakyas, accomplisher of all goals, son of suddhodana, of Gautama’s line, friend of scholars, son of mayadevi.

In some of the Puranas, in one he is described as having taken birth to "mislead the demons":
mohanartham danavanam balarupi pathisthitah
putram tam kalpayamasa mudhabudhirjinah svayam
tatah sammohayamasa jinadyana suramsakan
bhagavan vagbhirugrabhirahimsa vacibhirharih
(Brahmanda Purana)

In order to delude the demons, he (Lord Buddha) was present in the form of a child on the way while the fool, jina (a demon), imagined him to be his son. Later on, Lord Sri Hari (as avatara-buddha) expertly deluded jina and other demons by his strong words of non-violence.

A similar episode is found in the Linga Purana, which says Sakyamuni was sent to preach in the demon realms, which resulted in Shiva being able to destroy Tripura.

The name of the Buddha appears in the verse that describes the ten avataras in Srimad Bhagavatam:

matsya kurmo varahasca nrisimha vamanastatha
ramo ramasca ramasca buddha kalki ca te dasah
Here the Buddha is said to have taken birth to restore the 'Devas'.
tatah kalau sampravritte sammohaya sura-dvisham
buddho namnanjana-sutah kikateshu bhavishyati
(srimad-bhagavatam 1.3.24)

Then, in the beginning of Kali-yuga the Lord will appear as Lord Buddha, the son of Anjana, in the province of Gaya (Bihar) just for the purpose of infatuating those who are envious of the devas.

This topic as been much of debate.

Some have even claimed Balarama to be the 9th. incarnation of Vishnu and not Buddha.

However, the concept of God incarnating to lull people into darkness is indeed an interesting concept. It does bring a a parallel between Mohini and Buddha on these grounds. However, it would be extremely unfair to draw such a parallel here because the perfection of spiritualism taught by Buddha seems to be an extremely unlikely a work of deceit.

Views are most welcome on this subject.

~Souvik