Is your gun a single barrel shotgun, double barrel shotgun or a falling block rifle?
Davenport firearms was in business from 1880 to 1901. The company was taken over by Hopkins and Allen in 1901. They continued making the Davenport guns until 1915.
The single barrel shotguns were made in 10, 12, 16, and 20 gauge with barrels from 26" to 36" (Goose Gun) The finish was Blued and case hardened with walnut stocks and forends.
The current value for Very Good condition is $550, Good condition is $400, Fair condition is $250 and Poor condition is $100.
Add $100 for a Goose Gun in Very Good condition.
Values are from the Standard Catalog of Firearms. The Blue Book does not list Davenport Firearms.
I hope this helps you,