From Jīva Goswāmī's commentary on the Bhāgavata (10.3.1):
atra viśeṣaś coktaḥ kha-māṇikya-nāmni jyotir-granthe—
uccasthāḥ śaśi-bhauma-cāndri-śanayo lagnaṁ vṛṣo lābhago
jīvaḥ siṁha-tulādiṣu krama-vaśāt pūṣośanor āhavaḥ |
naiśīthaḥ samayo’ṣṭamī-budha-dinaṁ brahmarkṣam atra kṣaṇe
śrī-kṛṣṇābhidham ambujekṣaṇaṁ babhūd āviḥ paraṁ brahma tat ||
In the Kha-maṇikya astrological text it is said “The Moon, Mars, Mercury and Saturn were exalted. The ascendant was Taurus. Jupiter was in Pisces. The sun was in Leo, Venus was in Libra, and Rāhu was in Scorpio. It was the eighth tithi of the waning phase of the moon, on Wednesday, with the moon in Rohiṇī constellation. Kṛṣṇa was born at midnight with these auspicious arrangements.”
vṛṣakanyā-tulā-mīna-rājeṣu sphuṭam uccagāḥ |
soma-saumya-śāni-kṣoṇī-sutās taj-janmani sthitāḥ ||
yasmād viśvāvasau varṣe janma śrī-nanda-janmanaḥ |
viśvam eva vasu-śrīmad babhūvāmuṣya tuṣyataḥ ||
Elsewhere it is said: “The Moon, Mercury, Saturn, and Mars were situated in Taurus, Virgo, Libra and Capricorn respectively. The birth of Kṛṣṇa in the year of Viśvavasu (Jupiter’s 39th year), satisfying the universe, was endowed with excellent beauty."
So the rāśi is Taurus (Vṛṣa)
Rāmāyaṇa, Bāla-kāṇḍa 18.9 (http://www.valmikiramayan.net/utf8/baala/sarga18/balasans18.htm#Verse9) says that Lord Rāma's rāśi is Cancer (कर्कटे लग्ने वाक्पता इंदुना सह) (courtesy of Keshav Srinivasan)
Also "Rāmārcana-candrikā" as quoted and explained in Rūpa Gosvāmī's Laghu-bhāgavatamṛta (1.5.28):
uccasthe graha-pañcake sura-gurau sendau navamyāṁ tithau
lagne karkaṭake punarvasu yute meṣaṁ gate pūṣaṇi |
nirdagdhuṁ nikhilāḥ palāśa-samidho medhyādayodhyāraṇer
āvirbhūtam abhūd apūrva-vibhavaṁ yat kiñcid ekaṁ mahaḥ ||
"Rāma appeared with indescribable glory, possessing unprecedented powers, qualities and form, like the fire from the pure kindling stick of Ayodhyā for burning the demons, on the ninth lunar day, when five planets were exalted and the moon was conjoined with Jupiter in the ascendant of Cancer in the constellation Punarvasu. The sun was in Aries."
Baladeva Vidyābhūṣaṇa's commentary on this verse:
"He was born on the ninth tithi of the waxing moon during the Caitra month. The sun, Mars, Jupiter, Venus, and Saturn were exalted respectively in Ares, Capricorn, Cancer, Pisces and Libra. Jupiter was in the ascendant with the moon. Sun was in the tenth degree of Aries, Mars was in the third degree of Capricorn, Jupiter was in the twenty-eighth degree of Cancer, Venus was in the twenty-seventh degree of Pisces, and Saturn was in the twentieth degree of Libra."