Under Amaymon, King of the South
Cornyx only appears in the oddball Book of Oberon, as follows:
“He appeareth like a captayne, & he hath power to call together byrdes & that to one
place, & to take them, & he hath under [him] 7 legions.”
So, he looks like a captain, conjure what you will from that.
Very much a stub entry from the long list of fun things added by the Book of Oberon to the demonologies. He can call birds to one place and take them somewhere else. So, if you need birds, this would be the right demon to call upon.