The Wasserstein plate linked in a reply - and similar mounting products - require you to use the original main OEM metal plate with them. They are used to mount the OEM plate to various surfaces. They don't signal your doorbell into its "mounted" and ready-to-function state, and they don't attach directly to the doorbell for mounting purposes.
I could not find a source for the main OEM plate that latches to the doorbell and signals the device that it is "mounted" so it is ready to function, so I figured out a DIY. I also do not believe Brad's linked request form will get you a plate for the used device you purchased from ebay. Even folks who paid full price for a new product from authorized retailers don't seem to have luck when the latching mechanism fails after the warranty period.
Since the mechanism that latches the doorbell to the OEM plate will often fail, it is good to know: neither the latching mechanism, nor an OEM plate are needed to signal the device to function. You can just use a small magnet to make the doorbell think it is on the original plate. If you are looking at the back of the unmounted doorbell, the internal magnet-operated switch is in the upper right area. Not at the very top, but slightly above and to the right of the right-hand wiring screw/hole. If you use a flat-ish magnet and move it around that vicinity, you will hear the click of the internal switch and see the camera come on and the light turn green when you find the right spot. Tape the magnet in that spot so it doesn't slide around or jump to nearby metal. (I use just a small piece of good duct tape - don't glue it, or use super tape - as you will remove the magnet to charge.) Then, mount your door bell in any way you like. For one of mine, I used a hose-clamp type metal strap that goes through two slots in a cute mounting board I made with a little roof. I bought a silicone cover for the doorbell that hides the metal strap and also gives a bit of rain protection. I can also just set doorbell cams where I want them, when I want to - car seat, indoors, flower pot, wedged under a balcony, etc. You can mount with velcro, or build a housing that goes around the device, etc. If you are building a housing for it, just be sure to test with the camera to be sure your housing idea doesn't protrude too much into the fish-eye view.
