Is dygnets meny also acceptable?
No. Dygn is a very specific term for a period of 24 hours.
What exactly is wrong with "Kocken presenterar menyn för degan"? I even asked Google Translate after being marked wrong (because I am that sad) and it translated it into English exactly as this question asks it.
That is an accepted answer, given that you write it "dagen" and not "degan".
It seems that Swedes prefer not to say "the something of the something." It is always "the something's something." In Swedish of course!
This literally means: The cook is presenting the day's menu.
Dagsmenyn also acceptable?
Theoretically yes, but as far as I know it is never used.
Would "ser" be acceptable?
Instead of presenterar? No.
Would meny dagens work here?