Broadly, there are two different
opinions within the Sri Vaishnava tradition. One can be called the Mannar'
tradition, the other the 'Tolappar' tradition. In a nutshell, the difference
stems from lunar vs. solar month and whether to take sunrise or moonrise into
consideration for determining jayanti.
The Mannar tradition is followed
by Sri Parakala Mutt and 'munitraya' tradition Sri Vaishnavas such as both Andavan
Ashramas and most Vadagalai
acharya-purusha families. It is named after one Mannar Swamy of unknown date
who is the first extant authority arguing for this calculation. Mannar Swamy is
known to have very eminent predecessors who shared his opinion, such as the
Upanishad Bhashyakara Ranga Ramanujacharya.
Observation
1) The ideal date is the
conjunction of Rohini Nakshatra and Krishna Ashtami that lasts from sunrise
through the night. (This need not happen in the solar month of Avani. Lunar
month of Shravana before Avani is also okay according to this custom).
2) If (1) is not possible, if at
moonrise it is Rohini as well as Ashtami, that date should be taken. Neither
the Rohini nor the Ashtami need be pure as in the Tolappar tradition.
3) If (2) is not possible, if there is any conjunction of Ashtami and Rohini day or night, that calendar day should be taken as Sri Jayanti.