Kougaiji - Yaone is completely, totally loyal to Kougaiji. I suspect she has a bit of a crush on him. Kougaiji is protective of her, but he also seems to know when she needs to do something on her own.
Doukugakuji - They are obviously very good friends and completely trust one another, united in their loyalty to Kougaiji.
Lirin - Yaone is often relegated to watching over Lirin and keeping her out of trouble - not that that works. They seem to have an almost sisterly relationship.
Hakkai - I call Yaone and Hakkai "The Mutually Polite Society". Hakkai is her opposite number in Sanzo's group, and they often wind up either fighting or working together. I think there are definitely hints of a potential romance between them, although any romance involving Hakkai would have to conquer the barrier of Kanan's memory.