I would like to write most probable refutation Buddhist doctrine by Vaishnavaism.
Buddhists teach, that there are two types of arising (samudaya),
namely external and internal. The external arising refers to things
such as the earth, rivers, oceans and so on. These are made of four
kinds of minute particles (paramāṇus) namely earthly, watery, fiery,
and windy types. The internal arising refers to mind (citta) and
memory (caitya). This internal arising is made of five types of
aggregates (pañca-skandha), namely form (rūpa), consciousness
(vijñāna), sensation(vedanā), perception (samjñā) and mental
impression (saṃskāra).
We first reject the theory of creation based on minute particles and aggregates. These elements cannot create the universe because according to Buddhism there is no agent
that puts them together. We also reject the possibility that the Buddha could fulfill
the role of cosmic agent, pointing out that according to Buddhist theory everything is momentary. If the cosmic agent were momentary, he could not have a desire for creation. The underlying assumption is that a momentary agent cannot have such a desire because to desire something requires the continued existence of the desiring agent. After rejecting what we perceive to be the Buddhist theory of creation, we now proceed to refute the Buddhist theory of causation, namely the doctrine of interdependent origination. According to this Buddhist doctrine, ignorance (avidya) is the ultimate cause of our samsaric experience.
We quote
उत्तरोत्पादे च पूर्वनिरोधात् (Brahma Sutra 2.2.20)
Which means "Ignorance and so on do not explain causality" because the preceding one is destroyed when the subsequent one arises.” The Buddhist theory cannot explain causality:
(1) since a momentary (kṣaṇika) cause cannot be the material cause due to the fact that it is not connected to the effect that exists in a later moment, (2) since only a cause that is connected to an effect can be the material cause, (3) since an effect cannot arise without that [i.e. a cause connected to the effect], and (4) because with the destruction of such cause the connection [between the cause and the effect] is not explained. If everything is momentary then there is no causality possible because there cannot be any contact between a cause and an effect. After refuting the Buddhist theories of creation and causality, we now move on to state that the goal of human life according to Buddhism is not worth pursuing.
The desire for the goal of human life, which is eternal and which has a single essence, does not arise for a self that is momentary. This is because such a self has the nature of complete suffering as it is afflicted with great calamity and because there is no self of its own after its [i.e. suffering’s] cessation. To explain, no one desires the destruction of the self. The Buddhist theory of momentariness amounts to the destruction of the self. No one wishes to attain such a state. The goal of human life, which is eternal and which has a single essence is to attain Lord Narayana who is ocean of innumerable auspicious attributes which are intrinsic to His nature and cannot be surpassed — some of them being; omniscience, omnipotence, sovereignty, energy, creative-potency and glory. He is a repository of limitless perfections such as radiance, beauty, fragrance, tenderness, pervading sweetness and youthfulness.
There are four types of meditations which Buddhists practise, namely
meditation on one’s characteristics (svalakṣaṇa), on momentariness
(kṣaṇika), on suffering (duḥkha) and on emptiness (śūnya).
We reject these four types of meditation on the grounds that they lack scriptural support of the Vedas and the Upaniṣads (aprāmāṇikatvāt). They are ineffective practices because the objects of meditation are wrong. Proper object of meditation is the Lord alone.
I know the great Purusha, who is luminous, like the sun and beyond
darkness. Only by knowing Him does one pass over death; there is no
other way to the Supreme Goal. (Svetasvatara Upanishad 3.8)
The Blessed Lord said: Those who fix their minds on Me and always
engage in My devotion with steadfast faith, I consider them to be the
best yogis.(BG 12.2)
There are those who always think of Me and engage in exclusive
devotion to Me. To them, whose minds are always absorbed in Me, I
provide what they lack and preserve what they already possess. (BG
9.22)