It could be that the animal was doing a lot of hard work or running around, which made it exhausted. Or perhaps it didn't eat well and has no energy.
The cartoon animal might be tired because it was involved in a challenging game or competition that took a lot out of it. Maybe it also had trouble sleeping the night before.
A tired elephant cartoon might be popular, especially if it shows the elephant trying to rest but still having funny or sweet moments. People like seeing animals in vulnerable or relaxed states.
Maybe it's because yawning shows that the animal is really exhausted and needs rest. Simple as that!
Well, a cartoon of a cat laying down with its eyes half-closed and a lazy expression could show a tired animal.
Maybe the animal had a long day of adventures and didn't get enough rest.
Maybe it's because they have wacky and unexpected elements that make us laugh and forget about being tired.
Maybe it's been playing all day and didn't get enough rest.
Often, it's the contrast between the tired state and the humorous situations they find themselves in. Like when a tired character tries to do something simple but fails in a comical way. Also, the dialogue or inner thoughts of the character can add to the fun.
Start with drooping eyelids and add some dark circles under the eyes. Make the eyes look a bit glazed over.
Maybe it's part of the character's design to stand out or convey a certain mood.
To draw tired cartoon eyes, make the upper eyelid lower and the lower eyelid kind of saggy. Add some shading or smudging around the eyes to give that worn-out effect. Also, the pupils might be a little unfocused.