Now your query is explicitly looking at only payments for year = 2010, however, I think you meant to have your Jan/Feb/Mar actually represent 2009. If so, you'll need to adjust this a bit for that case. Don't keep requerying the sum values for every column, just the condition of the date difference in months. Put the rest in the WHERE clause.
SELECT
SUM( case when DateDiff(m, PaymentDate, @start) = 0
then Amount else 0 end ) AS "Apr",
SUM( case when DateDiff(m, PaymentDate, @start) = 1
then Amount else 0 end ) AS "May",
SUM( case when DateDiff(m, PaymentDate, @start) = 2
then Amount else 0 end ) AS "June",
SUM( case when DateDiff(m, PaymentDate, @start) = 3
then Amount else 0 end ) AS "July",
SUM( case when DateDiff(m, PaymentDate, @start) = 4
then Amount else 0 end ) AS "Aug",
SUM( case when DateDiff(m, PaymentDate, @start) = 5
then Amount else 0 end ) AS "Sep",
SUM( case when DateDiff(m, PaymentDate, @start) = 6
then Amount else 0 end ) AS "Oct",
SUM( case when DateDiff(m, PaymentDate, @start) = 7
then Amount else 0 end ) AS "Nov",
SUM( case when DateDiff(m, PaymentDate, @start) = 8
then Amount else 0 end ) AS "Dec",
SUM( case when DateDiff(m, PaymentDate, @start) = 9
then Amount else 0 end ) AS "Jan",
SUM( case when DateDiff(m, PaymentDate, @start) = 10
then Amount else 0 end ) AS "Feb",
SUM( case when DateDiff(m, PaymentDate, @start) = 11
then Amount else 0 end ) AS "Mar"
FROM
Payments I
JOIN Live L
on I.LiveID = L.Record_Key
WHERE
Year = 2010
AND UserID = 100