Postgres not returning data on array_agg query as below
A LEFT JOIN can solve it, like Laurenz provided.
But I suggest an ARRAY constructor in a LATERAL subquery instead:
SELECT l.name, b.book_list
FROM   library l
CROSS  JOIN LATERAL (
   SELECT ARRAY(
      SELECT title
      FROM   books
      WHERE  library = l.id
      )
   ) b(book_list)
WHERE  l.id = :library_no;

This way, you don't need to aggregate in the outer query level and don't need to GROUP BY there.
You also don't need COALESCE, since the ARRAY constructor over an empty result already produces an empty array ({}).
And it should be faster for a small selection in library - obviously the query gets the result for a single given library.
Aside, you only need the variable :library_no in a single place like demonstrated.
About LATERAL joins:

What is the difference between LATERAL and a subquery in PostgreSQL?

About the ARRAY constructor:

Why is array_agg() slower than the non-aggregate ARRAY() constructor?

Basic about joining tables in the manual.