Gunrunner61,
The two flat disks are not "coin" type buttons, or even buttons for that matter. They are in fact the base pieces from .50 caliber Maynard rifle/carbine casings or cartridges. The Maynard cartridge was not internally primed, therefore the firearm utilized a separate initial firing device, which caused a flash that ignited through the pinhole opening in the base of the cartridge (note the small hole in the center of your recovered disks). These disks were larger in diameter than the actual casing tube on Maynard cartridges, to facilitate removal of the empty casing after firing. These disks were originally attached to the base of the casing tube with solder. The effects of being buried in ground, along with moisture and temperature changes, results in the disks quite often being found separated from the casing tube.
The bullet on the right in your second photo, appears to be a .50 caliber Maynard.
Providing we have the honor of TheCannonballGuy also replying on this topic, more in depth information can assuredly be added regarding Maynard bullets, cartridges, and rifle/carbines.
The two button backs on the right side of your last photo, are from two-piece brass buttons. The face of the buttons is now missing, where the design detail would have been. One appears to be a blank back button, and the other appears to possibly carry a company mark in Raised Letter Depressed Chanel (RMDC) style.Although the complete marking is not legible in the photo, RMDC style markings are consistent for time frame on buttons beginning in the 1840's up to the American Civil War. Most likely the buttons were originally plain eagle design, general service buttons.
CC Hunter
P.S. While I was typing my reply, TheCannonballGuy was also replying.
He's faster on the "draw" with guns!
Was she a cute one? 
Im not well versed on CW items being from South Florida so I may not be depicting the right item but you get the idea.
