Can I trap coyote year around ?

Yes, so long as you have a valid state trapping license and all the state trapping rules, and county, or city laws and ordinances are being followed.  Coyotes are listed as a predator and can be hunted/trapped year-long.  However, coyote pelts are only valuable from November - February and usually are trapped or killed at other times of year due to depredation concerns on domestic animals.  Private land trespassing laws are still in effect.