They make some larger Live Traps that You could use to catch the Coyotes and maybe with some donations from Your concerned Neighbors You could afford to buy several to set out?
They also make a very quiet .22 caliber bullet to use in putting down said Coyotes!
A crossbow would help a lot in killing the Coyotes quietly and they are easy to use and if equipped with a scope can reach out a lot further and be very accurate!