Yon debe usar UNION en la subconsulta y luego GROUP BY en SELECT:
SELECT my_date,
my_month,
SUM(credit),
SUM(debit)
FROM (
SELECT cc.credit_date as my_date,
MONTHNAME(cc.credit_date) as my_month,
ROUND(SUM(IFNULL(cc.credit_amount,0)),2) AS credit,
0 AS debit
FROM cust_credit cc
WHERE YEAR(cc.credit_date) = YEAR(NOW())
GROUP BY cc.credit_date,
MONTHNAME(cc.credit_date)
UNION
SELECT
cd.debit_date ,
MONTHNAME(cd.debit_date) ,
0 ,
ROUND(SUM(IFNULL(cd.debit_amount,0)),2)
FROM cust_debit cd
WHERE YEAR(cd.debit_date) = YEAR(NOW())
GROUP BY cd.debit_date,
MONTHNAME(cd.debit_date)
) as TT
GROUP BY my_date,my_month
