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Wiktionary
coconut shy

n. A traditional fairground amusement in which customers throw balls at a row of coconuts in an attempt to knock one off its support and thereby win it.

Wikipedia
Coconut shy

A coconut shy (or coconut shie) is a traditional game frequently found as a sidestall at funfairs and fêtes. The game consists of throwing wooden balls at a row of coconuts balanced on posts. Typically a player buys three balls and wins each coconut successfully dislodged. In some cases other prizes may be won instead of the coconuts.

The word "shy" in this context is an English term meaning to toss or throw.

Usage examples of "coconut shy".

I should imagine Lady Schrapnell will assign me to permanent coconut shy duty when she finds out the bishops bird stump wasnt there after all.

There was a coconut shy over in one corner, and here Peter shone, because he was an excellent thrower.

He was lounging by a coconut shy and she looked right at him and stiffened.