rhyme up

Verb

 * 1)  To make a non-rhyming song, poem, etc., into a rhyming one.
 * The song is good, but I still gotta rhyme it up.
 * 1)  To come up with a rhyme for (a word, name, person, subject, etc.).
 * He rhymed up the kid's name with funny words to make an improvised song.