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.
Well, a cartoon of a cat laying down with its eyes half-closed and a lazy expression could show a tired animal.
Maybe it's because yawning shows that the animal is really exhausted and needs rest. Simple as that!
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.
Maybe the dog had a long day of play and adventure, which made it exhausted.
You can start by sketching a simple outline of a character with drooping shoulders and closed eyes. Add some light shading to show fatigue. It's not too hard if you keep it simple.
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.