Yeah! Glossy heavy weight full-color postcards. And we want to be able to personalize the back. The back can have a "template" so the address and stamp area is designated. Most often postcards have a monochrome back, but some stock allows for the mirror-gloss, full color, UV coated front with a matte finish back, presumably a finish okay for writing on.
 
I have clients that order small quantities of this type of postcard from a local print shop- printed on a laser type of copier, so I know it CAN be done- and realistically cheap.