What do you mean by "shock"? You started this thread talking about using a .22 rimfire, and now you are wondering if the .303 would work. I'm not sure what it is that you don't understand about hunting coyotes that would prompt the question about shock.
Lots of moose have been killed with the .303 British (I assume you are referring to that version) so you can assume it will kill coyotes. You do, of course, have to hit them properly with any sized bullet.
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