Did the Prodigal Son Ever Say He Was Sorry?

In a manner of speaking, yes he did:

His son said to him, ‘Father, I have sinned against heaven and against you; I no longer deserve to be called your son.’ (Luke 15:21)

By admitting that he had sinned against his father and that he felt he no longer deserved to be called a son he was telling his father that he was sorry for his actions.