There's a bit of a shibboleth between spacers and yinrih who live planetside regarding body language. Spacers are more prone to gesticulate while talking. They may do this with only their front paws, or use all four paws and their tail at once. When on a planet's surface, they'll often stop and rear up when having a conversation in order to free up their paws to move around. Sometimes their rear paws and tail will even twitch as though they would be moving them too if they didn't have to support their weight and maintain their balance. If they can't rear up they might do a “tippy-taps” style motion while talking.
When casually greeting someone, most yinrih chuff (the same trilling nasal exhalation used as a phoneme). It fills the same niche as a human smile.
Yinrih can hiss, although this isn't used as a phoneme, at least in Commonthroat. A hiss can be either plain or trilled. A trilling hiss is used to express unwelcome surprise, similar to saying “ouch!” or “arrgh!”. A plain hiss can express other mostly negative emotions like frustration.
Quickly flicking the ears back and then returning them to their previous position is the equivalent to a shrug. Flicking just the left ear is like a wink. Tilting both ears forward and opening the eyelids wide is a sign of strong positive emotion.
Moving their head such that the muzzle traces an upper half circle or arc is the same as a human rolling the eyes.
Since yinrih don't have a concept of romantic love, prolonged physical contact between adults isn't a thing, but some gestures do involve brief contact between individuals. Flattening the ears and briefly touching the top of both individuals' heads together is somewhat similar to a handshake, but it's only done between previously acquainted individuals of equal social status. A similar gesture is performed between a subordinate and a superior, with the subordinate pressing the top of his or her head against the side or chest of the superior.
Adult yinrih are, as a rule, much more particular about their personal space, which causes problems when humans mistake them for dogs and try to go in for a pat on the head or scritch behind the ears. “I'm a person and I have personal space!” is the common response. This often goes unheeded by humans who don't know Commonthroat and mistake their annoyed protest as quiet yipping and grunting.
When kits are very very young, they will often be carried on their dam's back, yet another contributor to the yinrih's “dog possum” nickname. Older pups will intertwine their tail with a parent's tail while out and about, similar to holding hands for safety. Intertwining tails is also a comforting gesture, and may be done between adults, for example when comforting someone after a traumatic event.
Running the claws of the front feet through one's tail is a common way to fidget, as well as being a self-soothing gesture. Thumping the tail on the ground repeatedly is either a threat or a way to release pent-up frustration. Flicking one's own side with the tip of the tail, like a horse shooing a fly, is similar to a dismissive hand wave. (The word for this gesture is even used in the same way we would use the term “handwave” to brush off an inconsistency.) Flicking someone else's side with the tip of the tail is a very rude gesture indicating the the person so flicked is both a nuisance but is easily “dealt with”. It's the closest the yinrih have to flipping the bird.
The yinrih equivalent to kneeling in prayer is to lie flat on the ground, tail extended straight out behind, and all four limbs flat on the ground, getting as much contact between the belly and the ground as possible. Less pious humans refer to it as “the sacred sploot”. Another meditative posture, done in microgravity, is to coil the tail around a tail bar, face the the palms of the front feet outward with the inner and outer thumbs crossed over one another, and the rear paws either clasped together or with the palms of the rear paws pressed together. This is the usual posture taken by clerics during torpor. Being in microgravity means they don't tire out while doing it, and can maintain it for the whole 24-ish hours of their torpor.
The traditional introductory greeting gesture is to rear up on the hind feet and pat one's belly with the left forepaw twice. If you're familiar with the origins of the boy scout handshake (a normal handshake but done with the left hand) it's supposed to indicate trust. In the yinrih's case you're demonstrating that you trust the other party by exposing your belly. This is the gesture that goes with the traditional greeting “Light shine upon you, friend.”