The parrot in Hindu mythology is associated with Kama, the god of love. The reason for this could be its green feathers and red beak which associates it with fertility. Red beak represents the red earth before the rain and the green feathers represent the green earth after the rains. Red represents unfulfilled desire, full of yearning, while green represents fulfilled desire, full of joy.
Kāmadeva (Sanskrit: कामदेव) is the Hindu deity of love.
In the Puranas, Kama is the king and lord of the apsarases. He is pictured armed with a bow and arrows: the bow is often represented to be of sugar cane, the bowstring a line of bees, and each arrow is tipped with a distinct flower which is devoted to, and supposed to preside over, one of the senses. He is also often represented as a handsome youth riding on a parrot and attended by nymphs, one of whom bears his banner displaying the Makara, or a fish on a red background.
link: Kamadeva on Wikipedia