There is a couple of techniques that address the shortcomings the copper roller has; skin thickening and tightening. Is not enough to increse hydration or the capability of the skin to hold water. With age the collagen of the skin degrades, it's a support tissue with a honeycomb structure that holds water and keeps the skin tight.
That's why the eyes get bags with age, when collagen degrades the fat that formerly was around the eyes evenly, loses its support and flows to the lower part forming the bags. That's the cause for wrinkles as well and two very effective techniques that the medicine has discovered to recover the degraded collagen are microdermabrasion and phonophoresis. The first stimulates the collagen production through making microinjuries to the skin, the healing regenerates that lost collagen improving the wrinkles. The phonophoresis also has this effect but it is used together with microdermabrasion as a way to increase the skin permeability and improve the healing rate of the skin, carrying vitamins and nutrients more effectively. For this purpose another technique called iontophoresis is used which increases skin permeability through electric microcurrents. A simple Google Scholar Paper Search will allow you to verify how effective these techniques are, most of all when researchers have combined microdermabrasion with phonophoresis.
Good news is that there are devices that allow people to use these techniques at home safely and easily. One good example is this article about an ultrasonic skin scrubber that cites several studies about phonophoresis and microdermabrasion that back the claims made about the product and explains how to apply this phonophoresis technique at home very clearly through videos and diagrams.