I have the 17 Remington(necked down .222 Remington Magnum), which is basically the grown up 17 Fireball. I have owned 3 of them. As well, I know 4 others who have them and use them often. I don't think that I'd describe my 17 as any quieter than a 223; so I'm not sure how loud your Fireball will be.
17 Centrefires are good coyote guns, however, for consistent kills you'll want to stay with 25gr pills and heavier. The more you research these pencil guns, the more interesting stuff you'll find out about them. Also, if you reload, you can buy all different types of lead for them( 25- 30)gr pills. There's a fellow on this board who goes by the handle, "Snowshoes". He's used the Fireball for the past season and has killed a boatload of coyotes with this gun. He'd be a great guy to chat with more about this calibre.
Go get one and let us know how it performs for you.
Good luck to you!