Does an Engagement Ring have to be a clear Diamond?

The type of engagement ring fiancees' typically wear will vary depending upon the particular culture.

Engagement rings are jewelry that illustrate that the person wearing it is going to be married in the future. In the western cultures, engagement rings are worn only by the bride-to-be, and these rings may feature diamonds or other gemstones. In other cultures men and women wear matching rings. In some cultures, engagement rings are doubled up as wedding rings and no wedding band is used.

Naturally colored diamonds and even other stones are becoming an increasing modern choice:

Clear Diamonds are most common and traditional in Western Societies

(Rings by Tiffany & Co.)