I don't know what your definition of quite is in this regards. The 22's are smaller cases so less powder .......
you might just want to handload the 280 down to varmit/light bullets and work for a reduced powder load if noise is a problem. Otherwise if you can cut the distance in half, to 150 go with the .17HMR as this is designed to be a varmit gun out to 200 yards and very flat shooting and reasonably quiet. I shot at the range without any noticable problems as it is only slightly louder than a 22LR with a slightly sharper crack.
They say coyotes are a bit on the big side but based on what I have seen at the range I won't hesitate at 100 - 150 yards if given the opportunity.
Your 280 is a great caliber. Good Luck
Greg
"Getting close to the game is the joy of Bowhunting for me, the harvest is a bonus."

Live 15 ft Python after eating a small Antelope!