落ち着いて is the most commonly used phrase used to tell someone to calm down. However, there are several ways to simply state that someone is annoyed or overly upset. Eg. いらいら, 怒る{おこる}.
If someone is getting annoyed over trivial matters you can use the word 些細{ささい}to describe the matter.
彼は些細{ささい}なことで怒っている
He is angry over trivial matters.
There may be an even closer translation, but this one is pretty close.
You might be able to extend that to requests.
些細{ささい}なことで怒らないで
Don't get angry over little things.
But this might not be very natural. Usually if someone were getting uptight over little things I would probably tell them (if they were close) something like:
些細{ささい}なものに過ぎないよ。落ち着いてよ。
It's nothing more than a trivial thing. Calm down.
or
何もないよ。落ち着いて
It's nothing. Calm yourself.