Basically weld brackets on both sides of the body with a type of hinge then run a bent tube from one side to the other with a tire holder. Wasnt sure if mounting it close enough to pillar would support it. Not sure if making something swing out that much is a good idea either, just a way to try and be different...maybe idk

 

I'd rather have a swing out tire carrier mounted on the bumper personally. I've also been looking into some of the tire carriers Tire Gate makes that fit in a 2" receiver, something like they offer should be easy to make.
Something like in your pic would probably require a lot of bracing and support for the quarter panels, and being mounted like that, I know I would hit where it mounts on some trees while wheeling. Doesnt seem like the best design to me.

 

Add some sweet corner panel armor to it and you should be good to go. I kind a like your design, different.