Is there a word to describe a person who makes up nice quotations?
Someone who makes something up isn't quoting anything, but they might coin a particularly quotable phrase.
Such a phrase can be called an epigram,
a pithy saying or remark expressing an idea in a clever and amusing way
...and the person who concocts it is called an epigrammatist.
Depending on usage, perhaps you should coin a new word that fits with what you are writing. Sometimes the best usage of words is to create new words that others will understand even if they aren't part of the common vernacular.
The person is a quotemaster.
They are very quotiferous.
They are double plus quotable. (I love and hate Newspeak)