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.

IE
http://www.pyramydair.com/s/pre_packaged_deals/Benjamin_Marauder_PCP_Air_Rifle_Synthetic_Stock/6067


Just my 2 cents.