Wood rings?

Woodchuckcase -- 101 E. Superior St.: This recent startup based in St. Louis Park, Minn., designs and custom makes wooden cases for phones, tablets, laptops and headphones. They emphasize U.S.-made craftsmanship, using authentic and sustainable materials.

Or Hippie Dick.

There is a local woodturners club here in town that may have some members that make rings. You could try e-mailing dthallb @ msn.com to enquire. There is also a woodworker from Michigan who does podcasts and YouTube videos that makes wooden rings.

I had one made through Sivertson Gallery many years ago by a very talented (and reasonably priced) gentleman up the shore.  I can't recall his name, but if you contact the gallery, I'm sure they have his info.

I made my own wedding band this summer based loosely on the methods described in this instructable: http://www.instructables.com/id/Bentwood-Rings/

Making the band itself was pretty easy. I went to Eslabon Jewelry Designs (207 W. Superior Street, Suite 230, Duluth) to brainstorm ideas for a setting. Orlando was really helpful and did a great job creating a setting and mounting on the ring. 

All said and done the ring with setting cost around $100. The ring itself cost roughly $5 in materials and several hours of careful sanding...