Do a quick search in youtube. There are several videos of coyotes taken with an air rifle. Most are 25cal PCP. You can probably get the rifle for $500 but scope and pump (or tank) will get you closer to $750.
PCP guns are noisier than a 22LR and much louder than a CB Long.
Some might be. Others most definitely are not. A .25 cal Marauder is so quiet, and so unlike the report of a firearm, that the impact of the pellet will draw the most attention.