jolly up vs cheer

jolly up is not a noun while cheer is a noun.

Word	Noun	Adjective	Verb	Adverb
jolly up	No	No	Yes	No
cheer	Yes	No	Yes	No

As verbs, jolly up and cheer are synonyms defined as:

Other synonyms of jolly up include cheer up, jolly along.

jolly up (noun)	cheer (noun)
	the quality of being cheerful and dispelling gloom
	a cry or shout of approval

jolly up (verb)	cheer (verb)
cause (somebody) to feel happier or more cheerful	become cheerful
	spur on or encourage especially by cheers and shouts
	show approval or good wishes by shouting
	cause (somebody) to feel happier or more cheerful
	give encouragement to