Under very rare circumstances, where every thing goes perfectly, maybe sometimes.
Therefore the wise person would take the answer to be a definete NO.
Like Tom said, we owe it to our prey to give them as humane of a death as we can give them.
If you are too young to legally carry a rifle, get yourself a magnum or beslisle 220 and use that if you are afraid to dispatch them by blunt force trauma.
Just please don't use the bb gun, it is not powerful enough and could actually get you hurt if the wounded coyote decides to go crazy and pull out of the trap in his zeal to get you for wounding it.