Without knowing its size... it looks like an ironbacked rivet-button whose rivet-stud is broken out of its iron back. You can view a very similar one which was discussed here in the What-Is-It forum a few days ago... click on the photo three times for super-enlargement to see the multi-multiple concentric circles on its front. http://www.treasurenet.com/forums/what/409851-unknown-button.html#post3949720
If it is larger than the one in that photo (the US 5-cent coin shows its size), your ironbacked button is not a busted rivet-button, but is instead what button-collectors call a Fashion button, made for use on "stylish" civilian coats and jackets. Unfortunately, an ironbacked button with no backmark (telling a manufacturer/dealer's name) is very difficult to narrowly time-date. All I can say about yours is that I have not seen any pre-20th-Century buttons whose front shows only multi-multiple concentric circles (such as the 19 or 20 on yours). But I do not believe I've seen every version of pre-20th-Century buttons.