I can't find anything on Eastern Arms. It may have been a trade name or store brand. Even if by a known maker, it would probably not be possible to determine an manufacturing date.
Clark:
Jim is correct. According to my records Eastern Arms is a trade name used by Iver Johnson Arms and Cycle Works on shotguns and inexpensive revolvers made for Sears & Roebuck of Chicago.
I don't know how important it is that the gun be pre 1899, but who is prepared to argue either way? There is simply no proof of the manufacturing date.