Just figured out how to do this:
Offline franchise mode is what I do, so that's the context.
Create an owner for the team whose coach you want.
Fire your coach and hire one of the generic coaches that's immediately available.
Create another character, an owner, this time of the team you want to control ultimately.
Fire your current coach and hire the coach you fired from team one who you now want on your team.
Retire from the league as both owners and when you're retiring as the second and final owner, select "Create New Character."
Choose "coach" for the team you ultimately want to control, and you'll be able to be the newly reassigned coach on the team of your choosing.
I did it with Rex and the Raiders. So I started as NYJ owner, fired Rex and hired a generic coach that ran the 34 so their scheme would stay constant. I then started another character as OAK owner, fired Allen, and hired Rex. Then I quit out as the OAK owner, started a career as a coach, went down to OAK, and there was Rex as my coach.
Boom!
Now, you might question my decision-making ability, but Rex is a total Raider, and I'm happy with the move
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This is very easy to do, but it took a little creativity to think through.