I have always been moved by Cat Stevens' "Father and Son", especially after becoming a father and being able to relate to the "Father's" side of the song; whereas, I was once able to relate only to the "Son's" side.I must also truthfully say that one of my favorite songs about fathers (and the one I most relate to) is my own creation, "A Guitar Man Named Chet" which has little to do with Chet and much to do about my Dad.
(That is enough self-indulgence for tonight!)
Another good one was "Daddy's Hands" by Holly Dunn.
A song entitled "The Hawk" written by Kris Kristofferson (I've only heard Richie Havens version. What a Voice!) It seems to be a "father to his son" song. It is a great piece.
Speaking of "Father and Son", the worst cover I have heard of that song was by Johnny and June Cash.
Paul Overstreet has a very good father song "Seeing My Father in Me":; I think that is the title. It has strong Spiritual overtones (as does many of the "father" songs.)
There are many more; however that is all I can think of at this time.
khandu