If you need to do this frequently, I would probably add a computed column PaymentMonth
to the table:
ALTER TABLE dbo.Payments ADD PaymentMonth AS MONTH(PaymentDate) PERSISTED
It's persisted and stored in the table - so there's really no performance overhead querying it. It's a 4 byte INT value - so the space overhead is minimal, too.
Once you have that, you could simplify your query to be something along the lines of:
SELECT ItemID, IsPaid,
(SELECT SUM(Amount) FROM Payments WHERE Year = 2010 And PaymentMonth = 1 AND UserID = 100) AS 'Jan',
(SELECT SUM(Amount) FROM Payments WHERE Year = 2010 And PaymentMonth = 2 AND UserID = 100) AS 'Feb',
.... and so on .....
FROM LIVE L
INNER JOIN Payments I ON I.LiveID = L.RECORD_KEY
WHERE UserID = 16178