Usage patterns
〈人〉が不機嫌になるfor someone to become sullen/irritated
He became sullen after being kept waiting.
不機嫌な顔をするto make a sulky/displeased face
She stayed silent with a sulky look on her face.
不機嫌そうに〈動詞〉to do something in a way that looks sullen/irritated
He answered in a sullen tone.
〈人〉を不機嫌にするto put someone in a bad mood
That one remark put him in a bad mood.