Much depends on the terrain and also how a guy chooses to handle the coyotes. In other words, if you're in tight terrain where you can't see far and a coyote can quickly show up and also disappear it leaves little room to get an easy standing shot with a rifle, so a shotgun makes since. In more wide open country where a guy can usually see them coming for a long ways and can easily get them to stop for a standing shot at any given time, a shotgun doesn't make much since UNLESS a guy just wants to let them come all the way to the call then they can do that without worrying about things going bad at close range, then a shotgun is again a good choice to have handy.
The choice of the shotgun has NOTHING to do with fearing them, it has to do with getting them killed efficiently.