These come to us from Scholar Sid Madhu, who kindly recorded the following pronunciations:

Dasaratha: emperor of the Kosala country, with Ayodhya as the capital.
Kausalya: wife of D., and mother to Rama
Kaikeyi: wife of D., and mother to Bharatha
Sumithra: wife of D., and mother to Lakshmana and Sathrugna

Sumanthra: chief minister/adviser to D.
Vasishtha: roal priest to D.
Viswamithra: mentor to both Rama and Lakshmana
Kooni: the handmaid to Kaikeyi, and abused by Rama in his youth
Janaka: Kingo of Janaka
Sita: the foster-daughter of Janaka; also called Janaki

Soorpanaka: the demoness sister to Ravana (first appears to Rama as Kamavalli)
Kara: commander of Soorpanaka's demon army
Jatayu: the great eagle; is pledged to protect Dasaratha's children. He dies to tell Rama and Lakshmana what happened to Sita
Vali: ruler of Kiskinda and the giant monkey race
Sugreeva: Vali's brother who helps Rama overthrow him