Olive listening over the radio as Popeye gets the tar knocked out of him in Let's You And Him Fight.
A small one but Olive thinking Popeye's been torn apart by the giant bird (either that, or fried by the lava from the volcano) in Popeye the Sailor Meets Sindbad the Sailor, all the while Bluto / Sindbad laughs at the whole thing.
Olive: POPEYE! OH, POPEYE, MY POPEYE! COME BACK TO ME!!(cries, until Popeye comes back with the bird cooked like a chicken / turkey)note Popeye: "There you are, with gravy!"
Goonland - as in the movie entry below, Pappy's dismissal reduces Popeye to tears, muttering "He don't even know his own skin an' bones!"
How Green Is My Spinach. Seeing the saddened kid watching Popeye getting a horrific beatdown from Bluto.
Pip-eye, Pup-eye, Poop-eye an' Peep-eye. In that short, Popeye tries to get his nephews to eat their spinach. They refuse - even when he warns that he will spank them. When they still refuse, he knows he has to make good on his word. The closeup of Popeye crying makes it clear that he does NOT enjoy it one bit. He only wants what he believes is best for his nephews, and the cartoons in general seem to be anti-spanking.
And before that, his lamenting about taking Swee'Pea away from Olive Oyl.
Pappy flat-out refusing to acknowledge Popeye as his son (at first) is rather sad, especially since Popeye himself is so joyous to find his father.
The morning after Bluto and Olive's engagement party. Olive's family is getting stripped of most of their belongings while the Tax Collector is telling them how much each item is. Olive's mother notices Cole with the newspaper over his face. She angrily tells him to stop reading before ripping it from his hands, revealing the poor man is crying.