Getting a COI issued for a WC policy works the same as getting one for any auto policy. My WC is through ADP. I go through the online payroll portal, where there's a link that takes me to insurance, then a certificate form. Fill out the form and click send. Easy peasy.
Other companies may not offer that convenience, so you'd have to contact your agency to get a COI issued. They'll need the company info to whom you're issuing and should normally turn the request in an hour or so during business hours. Company info would include name, address, phone, fax, email etc. Ask for a copy, so you have evidence it got done and can supply it if the dog eats someone's email at the carrier.