You are definitely NOT going to want to use a .22 for coyotes, fox or wolf. ESPECIALLY WOLF! I consider .22 mag minimum for coyotes and fox, and would only use it out to 100 yards or so. For wolf I would say a minimum of .243, and even then are you sure its even legal to shoot a wolf in your state?
Wolf NO but .22 long rifle is ok for Coyotes & fox Here in NH we have a night season for yotes & you can only use rimfire or shotgun I know a lot of people who use .22's & work fine but our yote's may not get as big as in Wisconsin & you usually don't get long range shots