child's play vs diversion

child's play and diversion both are nouns.

Word	Noun	Adjective	Verb	Adverb
child's play	Yes	No	No	No
diversion	Yes	No	No	No

As nouns, diversion is a hypernym of child's play; that is, diversion is a word with a broader meaning than child's play:

child's play: activity by children that is guided more by imagination than by fixed rules
diversion: an activity that diverts or amuses or stimulates

Other hypernyms of child's play include recreation.

child's play (noun)	diversion (noun)
any undertaking that is easy to do	an activity that diverts or amuses or stimulates
activity by children that is guided more by imagination than by fixed rules	a turning aside (of your course or attention or concern)
	an attack calculated to draw enemy defense away from the point of the principal attack