Maharaja Kusha
Kusha was the eldest son of Shri Ram and Mata Sita. In original Valmiki Ramayana it's simply written Shri Ram gave North Kosala to Lava and South Kosala to Kusha to rule as it's Kings. Their married life or their life after Vaikuntha Gaman of Shri Ram is not mentioned.
However, as Kusha was the one who inherited the throne of Ayodhya, he is mentioned in detail in Ananda Ramayana, Raghuvansh and his genealogy is mostly present in Puranas and Shrimad Bhagwatam.
In Raghuvansh written by Kalidas, it's mentioned that when he was ruling in Kushavati, he was visited by deity of Ayodhya who pleaded him to return back as the glorious city got dilapidated after Shri Ram.
Now that powerful King Kusha, who was the banner of his family, who had implanted arrowheads in the hearts of his enemies, and who was a friend to his subjects, encamped on the outskirts of the city those armies which had waving banners. [16-37]
King Kusha, the son of Maithili, living in the residential city of Raghu-s which had been restored to its former splendour, did not covet for the city of the lord of heavens, namely amarAvati of Indra, or even for the city of god of wealth, namely alakA-puri of Kubera. [16-42]
Kusha eventually returned after discussing with his ministers and rebuilt the city to its former glory and became the most illustrious king in Aryavarta. He is called King of Kings and even Devtas in Ananda Ramayana.
- Lines shaped like the Srivatsa mark, thunderbolt (Vajra), discus (Chakra), lotus, fish, bow, and mace (Danda) are marked on his hands, indicating that he will be a king even among the gods. || 41 ||
- He has a complete set of thirty-two teeth in his mouth. His neck is beautiful like a conch shell. His voice is deep and resonant like that of a Krauncha bird, a kettle-drum (Nagada), a swan, and a thundercloud. From this, it is known that he will surpass all the kings of the world. || 42 ||
Mahadevi Champika
Champika, daughter of Maharaja Bhurikirti was his first wife and she chose Kusha in Swayamvar.
- Hearing these words of Nanda, Champika, with a smiling face, happily placed the bridal garland around Kusha's neck with her own hands.
- At that moment, various divine drums resounded, and the bards and panegyrists sang praises. Sitting in that assembly with his head bowed down out of shyness, the young Kusha looked exceedingly handsome.
Rishi Agastya told Shri Ram that Champika won't be having any sons but daughters only and therefore when he had left for Vaikuntha, Kusha would get a second wife named Kumudvati and she will give him sons. After that they had nine daughters together.
Kumudvati
After he became King of Ayodhya, Kusha got married to Naga Princess Kumudvati, sister of Naga King Kumud in a peace alliance when he had almost annihilated Nagas due to Kumudvati taking his lost golden arm- bracelet mistakenly when he was sporting in Sarayu river with Champika (and his junior wives in Raghuvansh).
The king did not bear loss of bracelet because it was the charm securing victory; further it was worn by his father Rama before him, but not because he was avaricious for gold pieces; for a firm-minded person, as the king was, equally valued perishable flowers and variable ornaments. [16-74]
Kumuda who spoke in this manner, and who returned the ornament to the king who in turn replied "you are praiseworthy and a relation of mine from now on..."; then accompanied by his kinsmen Kumuda formed an alliance with the king by procedurally giving over the jewel of his dynasty which was no other than his sister Kumudvati.
In this manner the Naga king Kumuda got the direct son of Seetha and Rama, the legitimate descendant of the ruler of the three-worlds, as his kinsman whereby Kumuda gave up the fear from the bird-vehicle of Vishnu, namely Garuda, who had been his enemy in consequence of the death of Kumuda's father; and Kusha too got Kumuda who was the fifth descendant of Takshaka, a legendary serpent king, as his kinsman whereby the vexatious problem with serpents is obliterated on earth and the king Kusha ruled the country to the utmost delight of his subjects. [16-88]
Kusha and Kumudvati (in Ananda Ramayana) had eight sons and a daughter named Champakmalini. In Raghuvansh their eldest son Atithi is mentioned who inherited the throne after Kusha died and Kumudvati followed him in death as she couldn't live without her husband.
Sources: Raghuvansh by Kalidas and Ananda Ramayana