Then there's "Papa, Can You Hear Me?" from "Yentl."

Genie

PS, as Joe O. said at the beginning of this thread, there are a lot of songs that mention father--and, I'd add, there are a lot of songs about the fatherland and "God, the Father"--but this thread is about finding songs with "father" [human, presumably] as the main or a major theme.

In that vein, I'd add "A Boy Named Sue."