As per Sathya Sai Baba, Narayan or Vishnu avatars are: Matsya, Kurma, Varaha, Narahari, Vaman, Parashuram, Rama, Krishna and Sai

I was debating with myself whether I should put up this post as it is somewhat sensitive. Finally I felt that as a social media writer on spirituality and religion, I should publish my views on it. Readers are always free to reject my views.

I very much like the Narayan Bhaja Narayan bhajan sung by Bhagavan Sri Sathya Sai Baba himself as it is about the avatars of Vishnu or Narayan (Narayan is one of the names of Vishnu, https://en.wikipedia.org/wiki/Narayana ), with the avatar being God taking a form (animal or human) to help devotees overcome difficulties and to restore (practice of) Dharma, as per Hindu faith.

https://en.wikipedia.org/wiki/Avatar gives some interesting info. about avatars. An avatar signifies (is) "the material appearance or incarnation of a powerful deity, goddess or spirit on Earth". The wiki page states that avatars are mentioned in Puranic literature (like Garuda Purana and Bhagavata Purana) but are not mentioned in Vedic literature.

As a youngster, what I was exposed to, was the Dashavatar belief. Relevant extracts from Dashavatara wiki page, https://en.wikipedia.org/wiki/Dashavatara are given below:

The Dashavatara (/ˌdəʃɑːvˈtɑːr/; Sanskrit: दशावतार, daśāvatāra) are the ten primary avatars of Vishnu, a principal Hindu god. Vishnu is said to descend in the form of an avatar to restore cosmic order.[1] The word Dashavatara derives from daśa, meaning "ten", and avatāra, roughly equivalent to "incarnation".

The list of included avatars varies across sects and regions [Ravi: perhaps it should be religions], particularly in respect to the inclusion of Balarama (brother of Krishna) or Gautama Buddha.

...

Most draw from the following set of figures, in this order:[7][8][9] Matsya; Kurma; Varaha; Narasimha; Vamana; Parashurama; Rama; Krishna or Balarama; Buddha[note 1] or Krishna; and Kalki.

[References:]

1. "Know About "The Dashavatara"~ 10 Avatars of Lord Vishnu in Hinduism". NewsGram. 5 June 2020.

7. Leyden 1982, p. 22.

8. Vaswani 2017, p. 12-14.

9. Carman 1994, p. 211-212.

--- end wiki page extracts ---

I roughly recall that as a boy I have read about the ten avatars as: Matsya (fish), Kurma (tortoise), Varaaha (boar), Narasimha/Narahari (man-lion), Vaamana (dwarf-god), Parushuraama , Raama (Rama), Krishna, Buddha and Kalki. I don't recall reading then that Balarama (elder brother of Krishna) was an Avatar.

I had some confusion in my mind even then about Buddha being an Avatar of Vishnu/Narayana but as I knew very, very little about Buddha then, as compared to my 'little more' knowledge then about Rama and Krishna, I tended to accept it (that Buddha was an Avatar of Vishnu).

Today I know a little about Buddha and his teachings. While I have great respect for Buddha and his teachings, I don't think they fit in with Hindu scripture like Vedas and Puranas. So I don't accept the view that Buddha was an Avatar of Vishnu or Narayana. But Buddha was a great spiritual master with a somewhat different approach than Hinduism of his times, and Buddhism today is a great religion but has a somewhat different approach from that of Hinduism today. So my not accepting Buddha as an Avatar of Vishnu is no disrespect at all to Buddha or Buddhism.

I also feel that while Balarama was a great person, I find it hard to accept him as an Avatar like Rama or Krishna.

Naturally, what Bhagavan Sri Sathya Sai Baba said on this, has been and would be a very powerful source of divine revelation to me. 

For many years, I have been fascinated by the Narayan Bhaja Narayan bhajan sung by Bhagavan Sri Sathya Sai Baba. http://saibaba.ws/bhajans/narayanabhajanarayana.htm gives us the text of the bhajan in Hindi using Latin (English) script, and its meaning in English. https://www.youtube.com/watch?v=Ylz7aQ2ngVM , 7 mins, 47 secs shows Bhagavan singing it. In this bhajan, Bhagavan mentions the avatars as: Matsya, Kurma, Varaaha, Narahari (Narasimha), Vaamana, Parashurama, Rama, Krishna and Sai (Narayan).

It does not add up to ten avatars but nine. However, I am comfortable with the above list of avatars and believe in it.

Past couple of days, I searched sssbpt.info website using Google search to check if Balarama or Buddha are named as an Avatar of Narayana by Bhagavan Sri Sathya Sai Baba, but I could not get suitable results.

Perhaps Sathya Sai literature does have such references but I could not come across it. I would be very happy if people who know about such references, share them as comments on this post.

[I thank Wikipedia and have presumed that they will not have any objections to me sharing the above extract(s) from their website on this post which is freely viewable by all, and does not have any financial profit motive whatsoever.]