a yellow streak
A tendency to be cowardly or easily frightened. She likes to strut around like she's the boss of the place, but she has a yellow streak running down her spine if you ever confront her on an issue. He knew what they were doing was wrong, but his yellow streak kept him from intervening.
a ˈyellow streak(disapproving) the quality of being easily frightened; cowardice: He won’t fight? I always thought he had a yellow streak in him.
Yellow is often used to describe somebody who is a coward.