Like "various" is a adj. for "books", 「いろいろ」 is also to be used before 「本」.
A) If to say "There are various books on the desk.", then it would be
B) If to say "Various books are on the desk", it would be
However, in my opinion, both of the sentences (in English and in Japanese) in B are weird.
Will it sound more normal if was said like this?
"Your books are on the desk"