Building on Export Postgres table as JSON, you can select the data you want from your table, convert it to JSON, and then copy it to a file. Here's a SQLFiddle showing the JSON conversion.
Let's play with
CREATE TABLE data (id integer, name varchar(255), quantity integer);
INSERT INTO data VALUES
(1, 'apple', 10),
(2, 'banana', 20),
(3, 'cherry', 30)
;
First, get the data into the format you want, with fewer columns and any name changes.
SELECT
name AS fruit_name,
quantity
FROM data;
Then, put this in a subquery and convert it to JSON.
SELECT row_to_json(fruit_data) FROM (
SELECT
name AS fruit_name,
quantity
FROM data
) fruit_data;
Finally, wrap everything in copy.
COPY (
SELECT row_to_json(fruit_data) FROM (
SELECT
name AS fruit_name,
quantity
FROM data
) fruit_data
) TO 'a.file';
This will print each row as JSON line by line to the file
{"fruit_name":"apple","quantity":10}
{"fruit_name":"banana","quantity":20}
{"fruit_name":"cherry","quantity":30}
Postgres can probably build these into an array before you output them, but I think it'd be simpler to postprocess the file into an array if that's the format you want.