It's not a button "cover," it is the brass front of a button whose thin sheet-iron back has mostly rusted away. Although it shows a crown, very-very few Military buttons have an iron back. Yours is a 20th-Century civilian clothing "Fashion" button, manufactured for use on coats & jackets.
The crown on your button is one of the Continental Europe (which excludes Britain) royal crowns. ONE part of European crown emblems that can identify which country it represents is the "details" at the base of the arches, where they join the headband. There's too much concretion in that area on your button for me to be sure which specific nation your button's crown represents. Out of all the possibilities, it SEEMS to most closely resemble the Italian royal crown on the World War 2 era Italian Air Force insignia in the photo below.
Crown-identification tip:
Check the "older" coins of various nations, which often showed the Royal (or Empirial) crown of the nation.