Assembly mate trouble

I am having some problems finding the way to create the mate I want.  Attached are the parts, assembly, and jpgs that hopefully makes it clear the points of contact.

The idea is the ring will slide down into the grove and will touch the rod at the at 4 different points. I want a tangent relation between the contact points on the ring along the 4 lines specified and along the highlighted radius surfaces of the ring.

Please let me know if you have any suggestions or want more information to make things clear.

Contact points: ring

contact points: rod

SolidworksAssemblies