I'm aware of atleast two Vaishnava Sampradayas that accept Jivanmukti i.e. the Gaudiya Vaishnavas and the followers of Swaminarayan Sampradaya.
GAUDIYA VAISHNAVA SAMPRADAYA
Sri Rupa Goswami explicitly talks about Jivanmukti in His "Bhakti-rasāmṛta-sindhu" where He states that it is achieved by devotion:
īhā yasya harer dāsye
karmaṇā manasā girā
nikhilāsv apy avasthāsu
jīvan-muktaḥ sa ucyate
English Translation: "Anyone who, by his actions, mind and words, lives only for the transcendental loving service of the Lord, is certainly liberated within this life, even though he may appear to be actively engaging in material activities." (Bhakti-rasāmṛta-sindhu 1.2.187)
However, Gaudiya Vaishnavas also believe that it is possible for Jivanmuktas to fall from their liberated states. This is one big difference between the Jivanmukti of the Gaudiya Vaishnavas and the Jivanmukti of Advaitins. Jiva Goswami states in His "Bhakti Sandarbha":
jīvan-muktā api punar
yānti saṁsāra-vāsanām
yady acintya-mahā-śaktau
bhagavaty aparādhinaḥ
English Translation: Even if one is liberated in this life, by offending the Supreme Personality of Godhead he falls down in the midst of material desires. (Bhakti Sandarbha, Verse 111)
Srila Prabhupada also quotes a verse from an unnamed Purana to support this view in his commentary on the Chaitanya Charitamrita 3.8.26:
jīvan-muktāḥ prapadyante
kvacit saṁsāra-vāsanām
yogino na vilipyante
karmabhir bhagavat-parāḥ
English Translation: Even Jivanmuktas may fall down into material desires but those who are fully engaged in devotional service to the Supreme Personality of Godhead are not affected by such desires.
SWAMINARAYAN SAMPRADAYA
Sahajanand Swami is recorded to have advocated for Jivanmukti through Bhakti towards Sri Hari and the constant company of holy saints, various times in the Vachanãmrut. Some of such instances are:
The bhakta should firmly keep his mind at the holy feet of
Bhagvãn. Just as an iron nail that is firmly affixed to an iron surface
can never be separated, similarly, a person’s mind should be fixed
firmly at the holy feet of Bhagvãn. When the bhakta has kept his
mind at the holy feet of Bhagvãn in this way, he does not have to die
to attain the dhãm of Bhagvãn – he attains it while still alive.” (Vachanãmrut, Gadhadã III, Chapter 7, Verse 4)
“Therefore, even after attaining this satsang – which is rare for even
Brahmã – affection for objects other than Bhagvãn still remains. This
is because the person has not developed as firm a belief for the
pratyaksha svarup of Bhagvãn as he has for the non-pratyaksha
svarup of Bhagvãn. That is why the Shrutis state, ‘If a person develops
belief in his guru – who is the pratyaksha svarup of Bhagvãn – in the
same way that he has belief in the non-pratyaksha devs, then as a
result, he attains all the purushãrths (dharma, arth, kãm, and moksh)
which are described as attainable’. In fact, when he attains the
company of such a sant, he has attained He who was to be attained
after death, while still alive; he has attained that which is called
moksh or kalyãn, while being alive. (Vachanãmrut, Gadhadã III, Chapter 2, Verse 8)
“If a person is able to think about Bhagvãn in his antah-karans in this
way, and if he were to die while still holding such a desire for
Bhagvãn, he would definitely not have to take another birth. If he
engages in such dhyãn of Bhagvãn, he has certainly attained
Akshardhãm while alive. In addition, he can be said to be in the
process of becoming a niranna-mukta just like the niranna-muktas in
Shvet-Dvip. Such a person performs the bodily activities that are
necessary without effort. In fact, a person who is able to think about
Bhagvãn’s svarup like this has become fulfilled and has nothing more
left to achieve. (Vachanãmrut, Gadhadã II, Chapter 48, Verse 3)
