I just scanned a few hundred songs that mention Dad or Father, etc. My favorite is Papa Was A Rollin' Stone but that does not fit my Father. Papa fits a certain experience in my life but not Fathers Day.
This is just a fun song. Harry Vanda and Georg Young did the writing and "Little" Stevie Wright sings his heart out.
There's one line in this song that compliments my Father and that applies any time. Friday On My Mind is Timeless.
See if you can find the line and please let me know your favorite Fathers Day song.