The four yuga-avataras are...

Expressions researched:
"Age of Kali, Lord Krsna assumes a golden color" |"As the white incarnation" |"Dvapara-yuga, the complexion is black, Krsna" |"Hayagriva in the Satya-yuga" |"In Satya-yuga the Lord appeared" |"In Treta-yuga, the Lord appeared" |"Kali-yuga, the complexion is yellow. Lord Caitanya" |"Kapiladeva" |"Lord Krsna personally appeared as Lord Caitanya Mahaprabhu" |"Lord Krsna, appearing in a blackish body" |"Treta-yuga, the complexion is red" |"pita (yellow) as Caitanya Mahaprabhu in Kali-yuga" |"rakta (red) in Treta-yuga" |"reddish incarnation" |"sukla (white) in Satya-yuga" |"syama (dark blue) in Dvapara-yuga" |"the Lord incarnates in four colors" |"the Personality of Godhead appears in a blackish hue" |"the prescribed color for different millenniums" |"yuga-avataras"

CC Madhya-lila

The four yuga-avatāras are:

CC Madhya 20.246, Purport:

The four yuga-avatāras are (1) śukla (white) in Satya-yuga (SB 11.5.21), (2) rakta (red) in Tretā-yuga (SB 11.5.24), (3) śyāma (dark blue) in Dvāpara-yuga (SB 11.5.27) and (4) generally kṛṣṇa (black) but in special cases pīta (yellow) as Caitanya Mahāprabhu in Kali-yuga (SB 11.5.32 and 10.8.13).

CC Madhya 20.329, Translation:

“O Sanātana, now hear from Me about the yuga-avatāras, the incarnations for the millenniums. First of all, there are four yugas—Satya-yuga, Tretā-yuga, Dvāpara-yuga and Kali-yuga.

CC Madhya 20.330, Translation:

“In the four yugas—Satya, Tretā, Dvāpara and Kali—the Lord incarnates in four colors: white, red, black and yellow respectively. These are the colors of the incarnations in different millenniums.

CC Madhya 20.331, Translation and Purport:

“"This child formerly had three colors according to the prescribed color for different millenniums. Formerly He was white, red and yellow, and now He has assumed a blackish color."

This verse from Śrīmad-Bhāgavatam (SB 10.8.13) was spoken by Garga Muni when performing the name-giving ceremony for Kṛṣṇa at the house of Nanda Mahārāja. The following two verses are also from Śrīmad-Bhāgavatam (SB 11.5.21, 24).

CC Madhya 20.332, Translation:

“"In Satya-yuga the Lord appeared in a body colored white, with four arms and matted hair. He wore tree bark and bore a black antelope skin. He wore a sacred thread and a garland of rudrākṣa beads. He carried a rod and a waterpot, and He was a brahmacārī."

CC Madhya 20.333, Translation:

“"In Tretā-yuga, the Lord appeared in a body that had a reddish hue and four arms. There were three distinctive lines on His abdomen, and His hair was golden. His form manifested the Vedic knowledge, and He bore the symbols of a sacrificial spoon, ladle and so on."

CC Madhya 20.334, Translation and Purport:

“As the white incarnation, the Lord taught religion and meditation. He offered benedictions to Kardama Muni, and in this way He showed His causeless mercy.

Kardama Muni was one of the prajāpatis. He married Devahūti, the daughter of Manu, and their son was Kapiladeva. The Supreme Lord was very pleased with Kardama Muni's austerities, and He appeared before Kardama Muni in a whitish body. This happened in the Satya-yuga millennium, when people were accustomed to practicing meditation.

CC Madhya 20.335, Translation:

“In Satya-yuga the people were generally advanced in spiritual knowledge and could meditate upon Kṛṣṇa very easily. The people's occupational duty in Tretā-yuga was to perform great sacrifices. This was induced by the Personality of Godhead in His reddish incarnation.

CC Madhya 20.336, Translation:

“In Dvāpara-yuga the people's occupational duty was to worship the lotus feet of Kṛṣṇa. Therefore Lord Kṛṣṇa, appearing in a blackish body, personally induced people to worship Him.

CC Madhya 20.337, Translation and Purport:

“"In Dvāpara-yuga the Personality of Godhead appears in a blackish hue. He is dressed in yellow, He holds His own weapons, and He is decorated with the Kaustubha jewel and the mark of Śrīvatsa. That is how His symptoms are described."

This is a quotation from Śrīmad-Bhāgavatam (SB 11.5.27). The śyāma color is not exactly blackish. Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura compares it to the color of the atasī flower. It is not that Lord Kṛṣṇa Himself appears in a blackish color in all the Dvāpara-yugas. In other Dvāpara-yugas, previous to Lord Kṛṣṇa's appearance, the Supreme Lord appeared in a greenish body by His own personal expansion. This is mentioned in the Viṣṇu Purāṇa, Hari-vaṁśa and Mahābhārata.

CC Madhya 20.339, Translation and Purport:

“By this mantra, the people worship Lord Kṛṣṇa in Dvāpara-yuga. In Kali-yuga the occupational duty of the people is to chant congregationally the holy name of Kṛṣṇa.

As stated in Śrīmad-Bhāgavatam (SB 12.3.51):

kaler doṣa-nidhe rājann asti hy eko mahān guṇaḥ

kīrtanād eva kṛṣṇasya mukta-bandhaḥ paraṁ vrajet

"My dear King, although Kali-yuga is full of faults, there is still one good quality about this age. It is that simply by chanting the Hare Kṛṣṇa mahā-mantra, one can become free from material bondage and be promoted to the transcendental kingdom." Thus in Kali-yuga one worships Lord Kṛṣṇa by chanting Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare. To propagate this movement, Lord Kṛṣṇa personally appeared as Lord Caitanya Mahāprabhu. That is described in the following verse.

CC Madhya 20.340, Translation:

“In the Age of Kali, Lord Kṛṣṇa assumes a golden color and, accompanied by His personal devotees, introduces hari-nāma-saṅkīrtana, the chanting of the Hare Kṛṣṇa mantra. By this process He delivers love for Kṛṣṇa to the general populace.

Sri Caitanya-caritamrta Lectures

Lecture on CC Madhya-lila 20.330-335 -- New York, December 23, 1966:

Yugāvatāra means just like there are four yugas: Satya, Tretā, Dvāpara, Kali. The ages of each yuga we have mentioned already. Now in the Satya-yuga, when the yugāvatāra comes, He is white. He is Hayagrīva in the Satya-yuga, as white as our Hayagrīva brahmacārī. Yes. He is white. And rakta. Śukla-rakta-kṛṣṇa-pīta-krame cāri varṇa. In the Satya-yuga when the incarnation of yugāvatāra comes, His complexion is white. And in the next yuga, Tretā-yuga, the complexion is red. And the next yuga, Dvāpara-yuga, the complexion is black, Kṛṣṇa. And the next, Kali-yuga, the complexion is yellow. Lord Caitanya is yellow.