Which King is depicted with only one eye showing in a standard deck (most common) of playing cards?

Only the King of Diamonds is depicted with one eye in a standard deck of playing cards. Two of the Jacks have one eye, the Jack of Spades and the Jack of Hearts. All of the Queens are shown with both eyes.

The deck of 52 playing cards, sometimes called the "French" deck, is the most common deck of playing cards used today. It includes thirteen cards of each of the four suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠), with reversible "court" or face cards i.e. they appear the same turned upside down. Some modern designs, however, have done away with reversible face cards. Modern playing cards carry labels on opposite corners (rarely, all four corners) to facilitate identifying the cards when they overlap and so that they appear identical for players on opposite sides. The most popular stylistic pattern of the French deck is sometimes referred to as "English" or "Anglo-American playing cards".

There does not appear to be any specific reason the faces of the cards are drawn this way except historical tradition.