There are suggestions that Dasaratha promised Ashwapathi( Kaikeyi's father) that he will crown Kaikeyi's son after his time. This would actually validate Kaikeyi's claim to the throne then.
Rama uses this line of argument to console Bharatha when they meet in the forest. Rama seems to have used this tactic to dissuade Bharata from feeling guilty.
There is no evidence of this in Valmiki's Ramayana even though Rama seems to have uttered it.
- Kaikeyi would not have needed to use the couple of boons if she was sure of this word from Dasaratha to her father. Dasaratha was known anyway to keep his word and wouldn't have retracted if he had given that promise to her father.
- Manthirai, Kaikeyi's aide was not aware of this promise. She was someone who knew everything about Kaikeyi's life.
- Vasishta and Sumanthirar, both knew everything about Dasaratha never said anything regarding this promise.
- Even when Bharatha blasted Kaikeyi, she never said anything about this promise