We are aware of Tantras in Saivism but there seems to be no Tantras associated with Sri Vaishnavam.
We have Tantras of Ganesha, Subrahmanya, Devi,Shiva to cite a few.
There seems to be a Narayana Tantra and I am researching on this.
And there is
Vaishnava-Sahajiya is a form of tantric Vaishnavism that centred in Bengal, India. It had precursors from the 14th century, but originated in its definitive form in the 16th century. Vaishnava-Sahajiya is generally considered as a ‘left-hand path‘ (Sanskrit:vāmācāra) and apostate (Sanskrit: apasampradaya; see Sampradaya) from the “orthodox” or vedic standpoint, though followers claim that this view stems from a superficial understanding. There are both right-handed and left-handed Vaishnava-Sahajiyas Dakshinachara may be rendered into English as “right (Dakshina) (path to) attainment (chara)”, while Vamachara may be rendered into English as “left (vama) (path to) attainment (chara)”. The Dakshinacharyas (“Right Attainers”) are the ones that practice the Panchamakara (‘Five Ms’) symbolically or through substitutions, whilst the Vamacharyas (“Left Attainers”) are the ones that practice it literally'( wiki)
There is Narayana Tantra which deals with Tantra.
Even in this only basic aspect is referred.
There is no elaborate description of Tantra Sri Vaishnavam.
One finds elaborate description of Tantra aspects of Hinduism in Saivite texts, Shiva, Shakti,Ganapati,Subrahmanya.
But this aspect is noticeably absent in Sri Vaishnavam.
When one checks with the Vedas the Tantric aspect is found, though not in greater details.
They are hidden in the Mantras which ,later have been explained by the Bhasyas,the elaborate commentaries.
One also finds detailed texts in Tamil, including that that of Siddhas about Tantras.
There is a school of thought which believes the Tantras might have been in vogue even before the Vedas!
Such being the case, why no Tantra system is found in Sri Vaishnavam?
Vedas, unlike other Religions, is born out of Experience, Anubhuthi and Intutuion.
The experiences are were recorded by the experienced/Realized Souls.
As Hinduism is fundamentally a personal one and not an Institutionalized one, the experiences are vast.
Individuals realized Brahman through Many ways.
As Lord Krishna states that One chooses the method according to one’s Swabhava, Disposition.
All different forms of worship, the attempt to realize Brahman, The Reality were categorised braodly into four.
Gnana Yoga, Path of Knowledge, where one realizes through wisdom and discrimination,
Karma Yoga, Path of Action, by performing dispassionate action,
Raja Yoga, by discipling the Mind, through Physical and mental discipline and
Bhakti Yoga, path of surrendering oneself to Reality or God.
While Gnana Yoga is an Intellectual approach, Karma Yoga is an active approach which has more to do with co ordination of intellect and mind,Raja Yoga , co ordination of Body with Mind/Intellect, The Bhakti Yoga is to tally emotional, which probabaly is by far the most removed from Reasoning or Intellectual approach.
Despite our assertion and belief, it is emotion that really rules us.
It takes a conscious and deliberate, though a difficult one, step to follow the three Yopgas, Gnana,Karma and Raja.
But Bhakti Yoga is natural and easy to follow iof one is truly a believer.
Emotions , if one were to analyse, do not stand to reason.
If one were to analyse, emotions have no meaning.
But practiacl life teaches us otherwise.
We are ruled by emotions as they are instinctive and they are there for one’s welfare.
So Bhakti Yoga is very effective and it calls for total surrender to God/Reality.
The worhip of Vishnu leans more on Bhakti Yoga as the system of Visishtadwaita determines it.
To put it simply, with out going into philosophical differnces beteween Advaita and Visistatdwaita, Visistadwaita never really asubcribes to the view that one becomes the Reality or one, by getting rid of Ignorance, Avidya, one returns to the orginal state of Brahman.
So the emphasis on worship of the Supreme Power, Narayana, Visnhu or Krishna.
But, when one takes the stand of Advaita, one being a part of the ONE Reality. one starts practices taking on this premise that He is the Reality and engages himself in different systems of pratcie, Gnana, Karma ,Raja and Bhakti Yoga, depending on one’s dispostion,Swabhava.
As an extension of this thought, the Tamtra ,Yantar worship is more pronounced in Shaivism and not in Sri Vaishnavism.
Later Bhakti Yoga developed by Seerrs like Chiatanya in the north of Vindhyas and by the Azhwars in Tamil Nadu dveloped the system of Bhakti yoga in elaboration to such an extent that the worhsip has been more or less restrcicfted to this emotional approach to Reality.
So much the Krishna Cult, especially ISKCON, quote Caitanya and excerpts form srimand Bhagavtham to recoomend only Bhakti to Krishna, Vishnu though the Vedas do not support this exclusively.
‘ Tantra in Vaishnavism implies that Krishna Radha is an additional form of Shiva and Shakti. According to the Vaishnavas Krishna and Radha are two manifestations of a single absolute reality. The concept of Siva-Sakti in Tantra is supposes to have inspired the moulding of Krishna-Radha. A close relation with Shakta is revealed in the Panchratra works of the Vaishnavas. In both the traditions Lakshmi is considered as the Supreme Energy who resides in Muladhara. Similarly the Panchratra works provide for Nyasas as a means of Sadhana.
The body is regarded as the abode of God in Tantra. In the different chakras supposed to be within the body Saktidhama and Sivadhama are considered. In some Vaishnava Samhitas, Mathura, Vrindavan are regarded as the abode of God. Gokula has been described as God’s abode which is in the shape of a thousand-petalled lotus in some Puranas. In Tantra this lotus is called Sahasra- Padma which is believed to be within the head. The description of Vishnu and his Sakti, Lakshmi and their abode in the Brahma samhita is Tantric in spirit.
‘No one can introduce any new system into the Vedic way of life; if one does so out of malice, he is to be known as a pāṣaṇḍī, or atheist. In the Vaiṣṇava Tantra it is said:
yas tu nārāyaṇaṁ devaṁ
sa pāṣaṇḍī bhaved dhruvam
Although it is forbidden, there are many pāṣaṇḍīs who coin terms like daridra-nārāyaṇa and svāmi-nārāyaṇa, although not even such demigods as Brahmā and Śiva can be equal to Nārāyaṇa.
Sometimes in revealed scriptures Lord Śiva is described as being nondifferent from the Supreme Personality of Godhead. The point is that Lord Śiva and Lord Viṣṇu are so intimately connected that there is no difference in opinion. The actual fact is, ekale īśvara kṛṣṇa, āra saba bhṛtya: “The only supreme master is Kṛṣṇa, and all others are His devotees or servants.” (CC.1:5:142) This is the real fact, and there is no difference of opinion between Lord Śiva and Lord Viṣṇu in this connection. Nowhere in revealed scripture does Lord Śiva claim to be equal to Lord Viṣṇu. This is simply the creation of the so-called devotees of Lord Śiva, who claim that Lord Śiva and Lord Viṣṇu are one. This is strictly forbidden in the Vaiṣṇava-tantra: yas tu nārāyaṇaṁ devam (CC.2:18:116). Lord Viṣṇu, Lord Śiva and Lord Brahmā are intimately connected as master and servants. Śiva-viriñci-nutam (S.B.11:5:33). Viṣṇu is honored and offered obeisances by Lord Śiva and Lord Brahmā. To consider that they are all equal is a great offense. They are all equal in the sense that Lord Viṣṇu is the Supreme Personality of Godhead and all others are His eternal servants.
There are many Vaiṣṇava families in Bengal whose members, although not actually born brāhmaṇas, act as ācāryas by initiating disciples and offering the sacred thread as enjoined in the Vaiṣṇava tantras. For example, in the families of Ṭhākura Raghunandana Ācārya, Ṭhākura Kṛṣṇadāsa, Navanī Hoḍa and Rasikānanda-deva (a disciple of Śyāmānanda Prabhu), the sacred thread ceremony is performed, as it is for the caste Gosvāmīs, and this system has continued for the past three to four hundred years. Accepting disciples born in brāhmaṇa families, they are bona fide spiritual masters who have the facility to worship the śālagrāma-śilā, which is worshiped with the Deity. As of this writing, śālagrāma-śilā worship has not yet been introduced in our Kṛṣṇa consciousness movement, but soon it will be introduced in all our temples as an essential function of arcana-mārga (Deity worship).
(Sri Caitanya Caritamrta—–1:7:45—–purport).
References and citations.