The Bad Seed~At the end of the film, Patty McCormack is spanked because Rhoda has been such a bad girl. Basically, this was the Fifties, when a film about a murderous child would make people nervous, so they added this as a humorous(?) touch.
If I recall correctly, there are on-screen spankings in:
The Quiet Man~Doesn't John Wayne swat Maureen O'Hara? Later, the two battle, ending up in a famous scene in "McLintock!" (already listed).
Taming of the Shrew~various versions
Tom Brown's School Days (1940)
Careful, He Might Hear You
The Night of the Hunter
Yankee Doodle Dandy
The Seven Little Foys
A Home of Our Own
Exit to Eden *blush*
The Children's Hour
The Whipping Boy
Casey's Shadow
Kiss Me, Kate!
Barry Lyndon
Mrs. Miniver
In "The Curse of the Cat People", it occurs off-screen, when Amy refuses to say that Irena is an imaginary friend.
There are more films of people, especially children, being beaten with a cane, belt or strop in many period films. (A strop is the leather strip used for sharpening a razor for shaving.) Now, THAT is violent! Those include:
Lady Jane~Jane (Helena Bonham Carter) is beaten into submission by her mother in a harrowing, lengthy scene.
Wuthering Heights~both versions(?)
How Green Was My Valley
The Fool Killer
Pretty Baby
I have severe pain syndromes, so I especially remember such moments of physical distress during which I often mute the sound of simply close my eyes. As a child of the Fifties and being exceptionally stubborn, I also recall being spanked!