Purring, soft cooing or chattering, or a big, happy chicken smile. They are usually in a well relaxed state during a smile, and pull up their lower eyelid, which also pulls up their cheeks to a certain point. Since the beak is immobile and fixed, a smile is subtle, and can pass quickly, so can be hard for some people to catch when it's happening.
A few examples of chicken smiles:
Our little buddy, Big Red rooster, a balanced, hatchery PR male- a hybrid known for throwing aggressive males. He is a great communicator by body language. He knows how to ask for things- for instance, being picked up and treats. A happy fellow.
This BCM pullet smiles often.
Here, she's laying her first egg while her sister was there for support. The pullet cooed and made soothing noises to herself while smiling. If you look close, you can see the sides of her cheeks are pulled up in a big smile. Effervescent and literally glowed with happiness when her egg time finally came. She's like this everytime she lays. Never seen another pullet enjoy the egg laying so much.
Our BCM flockmaster. Literally the most gentle and kind alpha male we've had. If speaking to him he smiles in response. He jumps up and down in excitement like a dog when you visit his pen, or share a treat. Crows to you to visit if he sees you walking. He enjoys being held, and the hens seem bonded to him.
If they are squawking, depressed or hunched there is a problem.