rhyme up

verb2

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.
2. •
   To make a non-rhyming song, poem, etc., into a rhyming one.

   • The song is good, but I still gotta rhyme it up.