Coaster
wiktionary
From coast(“edge of the land where it meets an ocean, sea, gulf, bay, or large lake”) + -er( suffix forming agent nouns). [1]Coast is derived from Middle English coste(“rib; side of the body, flank; side of a building; face of a solid figure; coast, shore; bay, gulf; sea; concavity, hollow; boundary, limit; land; country; district, province, region; locality, place; division of the heavens; compass direction; direction; location with reference to direction, side”)[and other forms], [2] from Old French coste(“rib; side of an object; coast”) (modern French côte(“rib; coast; hill, slope”)), from Latin costa(“rib; side, wall”), [3] from Proto-Indo-European *kost-.
From coast(“to glide along without adding energy; to make a minimal effort; to slide downhill (especially, to slide on a sled upon snow or ice)”) + -er( suffix forming agent nouns). [1]Coast is derived from Middle English costeien(“to travel along a border or coast; to go alongside (something), skirt; to accompany, follow; to travel across, traverse; to be adjacent to, to border;”)[and other forms], [4] from Anglo-Norman[Term?], Old French costoier(“to be at the side of”)[and other forms] (modern French côtoyer(“to pass alongside; (figuratively) to rub shoulders”)), from Latin costicāre, from costa(“rib; side, wall”); see further at etymology 1. [5]
Sense 2.1 (“small stand or tray”) is from the fact that the object and the decanter or wine bottle on it “coast” or travel around a tabletop from person to person. [1] Sense 2.2.2 (“useless compact disc or DVD”) refers to the fact that the object is only useful as a drink coaster.
etymonline
coaster (n.)
1570s, "one who sails along coasts," especially one who trades from port to port in the same country, agent noun from coast (v.) in its sense "to go around the sides or border" of something. Applied to vessels for such sailing from 1680s.
The meaning "tabletop drink mat" to protect a wooden table surface from condensation, etc., was in use by 1913, extended from bottle-coaster "low, round tray used for a decanter" (1874); it was formerly on wheels and so called probably because it "coasted" around the perimeter of the table to each guest in turn after dinner.