The flat oval stone is made from calcified Chalcedony engraved with a portrait of Tigranes II of Armenia in profile to the right.
Dvin, the ancient capitol of Armenia

Dvin was one of the most ancient settlements of the Armenian Highland and an ancient capital of Armenia, traced back as far as the 3rd millennium BC. During the excavations of 1958, a settlement of Late Bronze and Early Iron age period was discovered under the citadel of Dvin. Excavations revealed ancient workshops and worship...
Ancient Armenian silver Goblet (7th-6th century BC.)

Silver Armenian golblet, Lori Berd 7th-6th centuries BC. – Museum of the History of Armenia, Yerevan
Silver medallion 2nd c. BC.
Silver medallion 2nd century BC, excavated in Sisian, Syunik region of Armenia. Depiction of a Golden Eagle clutching some type of wild cat, most probably a leopard. The symbolism of the Golden Eagle was important in pre-historic motif’s on the Armenian highland, as well as many of the Armenian Dynasties of the the old,...
Medallion from ancient Armavir
Armavir was one of the oldest and most sacred cities of Armenia. It was an ancient capital of Armenia, said to have been founded by King Aramais in 1980 B.C. In addition to its prominence as a capitol of Armenia, Armavir has served as a center of religious worship almost continuously from its establishment...
Bow and quiver form Armenia 14-12 c. B.C
I imagine Hayks bow must have looked somewhat similar to this one (only much larger as the legends describe).