I have the following query:
SELECT
SUM(\"balance_transactions\".\"fee\") AS sum_id
FROM \"balance_transactions\"
JOIN charges ON balance_transactions
Assuming I understand your request correctly I think what you need is something along these lines:
SELECT "periods"."start_date",
"periods"."end_date",
SUM(CASE WHEN "balance_transactions"."created" BETWEEN "periods"."start_date" AND "periods"."end_date" THEN "balance_transactions"."fee" ELSE 0.00 END) AS period_sum
FROM "balance_transactions"
JOIN charges ON balance_transactions.source = charges.balance_id
JOIN ( SELECT '2013-12-20'::date as start_date, '2014-01-19'::date as end_date UNION ALL
SELECT '2013-12-21'::date as start_date, '2014-01-20'::date as end_date UNION ALL
SELECT '2013-12-22'::date as start_date, '2014-01-21'::date as end_date UNION ALL
SELECT '2013-12-23'::date as start_date, '2014-01-22'::date as end_date UNION ALL
SELECT '2013-12-24'::date as start_date, '2014-01-23'::date as end_date
) as periods
ON "balance_transactions"."created" BETWEEN "periods"."start_date" AND "periods"."end_date"
WHERE "balance_transactions"."account_id" = 6
AND "balance_transactions"."type" = 'charge'
AND "charges"."refunded" = false
AND "charges"."invoice" IS NOT NULL
GROUP BY "periods"."start_date", "periods"."end_date"
This should return you all the periods you're interested in in one single resultset. Since the query is 'generated' on the fly in your front-end you can add as many rows to the periods part as you want.
Edit: with some trial and error I managed to get it working [in sqlFiddle][1] and updated the syntax above accordingly.