cheerlessness vs unhappiness

cheerlessness and unhappiness both are nouns.

Word	Noun	Adjective	Verb	Adverb
cheerlessness	Yes	No	No	No
unhappiness	Yes	No	No	No

As nouns, unhappiness is a hypernym of cheerlessness; that is, unhappiness is a word with a broader meaning than cheerlessness:

Other hypernyms of cheerlessness include sadness.

cheerlessness (noun)	unhappiness (noun)
a feeling of dreary or pessimistic sadness	emotions experienced when not in a state of well-being
	state characterized by emotions ranging from mild discontentment to deep grief