Yes, that is what partner trapping is you need to get the approriate form at Fish and Wildlife and have the senior partner sign it (as well as yourself).
I think the lience is only about $20.00
The trapping regs. are on line at sustainable resource managenment (SRD).
This should answer all your questions but I'm quiet sure you can only shoot "not trap" coyotes and beaver without a trapping lience.
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