what Double back tape for 3" car medallion

I usually keep a roll of outdoor mounting tape around. the stuff I have is clear silicone with red  film to keep from sticking to itself.

should be available at you local WalMart or big box home center.
tin

I'll give a thumbs up to the Scotch product noted above. I've used it to attach three sports medallions to a friend's truck here in East Central Florida (hot sun) and it's been through uncounted car washes (who counts car washes?) and it's holding great. We use Eclipse sunshades for our windshields and the adhesive provided with the product eventually releases. After a thorough cleaning of the surface and application of the Scotch Outdoor Mounting tape, it's back for good. The sunshades have spring retractors that pull the shade open when released. When the sunshade is "engaged," in the closed position, the springs are applying constant shear force on the adhesive, all day, in the hot Florida sun, and it holds great. I found it important for the brackets to be attached and allowed to bond for a day, but your medallion is not likely to have much force applied, so an instant stick-on would work just fine.

Three inches in diameter is seven square inches. That's quite a bit of gripping power. Another good aspect of the tape is that it can be sliced off carefully with a sharp knife or razor blade and the remnants removed if needed.

The other post about VHB tape is also true. I've used quite a bit of VHB backed DualLock stuff and it holds even stronger, although it's typically a good bit thicker and more expensive.