Having a quick look the procedure doesn't seem to use anything very special to SQL Server so I suggest just modifying the create command and see if it compiles.
In other words something like:
CREATE PROCEDURE TrialBalance()
BEGIN
SELECT COA_T .AccCode AS [Account Code], COA_T.AccName AS [Account Name],
CASE WHEN SUM (CASE WHEN COA_T.AccType in ('Cash & Cash Equivalents ','Marketable Securities','Accounts Receivable','Inventories','Prepaid Expenses','Fixed Asset','Intangible Asset','Investments','Other Non-current Assets','Accounts Payable','Accrued Expenses','Short-term Loans','Current Portion of Long-term Debt','Income Taxes Payable','Line of Credit','Term Loan','Capital','Current Year Earnings','Retained Earnings','Dividends','Share Capital','Paid in Capital','Open Balance','Sales Revenue','Operating Expenses','Administrative expenses')and COA_T.AccTransCate in ('BS','PL') and COA_T.AccTransSubCate in ('ASS','LBT', 'EQU', 'REV', 'EXP')
THEN DebitAmt-CreditAmt ELSE 0 END) > 0 THEN (SUM (CASE WHEN COA_T.AccType in ('Cash & Cash Equivalents ','Marketable Securities','Accounts Receivable','Inventories','Prepaid Expenses','Fixed Asset','Intangible Asset','Investments','Other Non-current Assets','Accounts Payable','Accrued Expenses','Short-term Loans','Current Portion of Long-term Debt','Income Taxes Payable','Line of Credit','Term Loan','Capital','Current Year Earnings','Retained Earnings','Dividends','Share Capital','Paid in Capital','Open Balance','Sales Revenue','Operating Expenses','Administrative expenses') and COA_T.AccTransCate in ('BS','PL') and COA_T.AccTransSubCate in ('ASS','LBT', 'EQU', 'REV', 'EXP')
THEN DebitAmt-CreditAmt end )) ELSE 0 END AS [Debit],
CASE WHEN SUM (CASE WHEN COA_T.AccType in ('Cash & Cash Equivalents ','Marketable Securities','Accounts Receivable','Inventories','Prepaid Expenses','Fixed Asset','Intangible Asset','Investments','Other Non-current Assets','Accounts Payable','Accrued Expenses','Short-term Loans','Current Portion of Long-term Debt','Income Taxes Payable','Line of Credit','Term Loan','Capital','Current Year Earnings','Retained Earnings','Dividends','Share Capital','Paid in Capital','Open Balance','Sales Revenue','Operating Expenses','Administrative expenses')and COA_T.AccTransCate in ('BS','PL') and COA_T.AccTransSubCate in ('ASS','LBT', 'EQU', 'REV', 'EXP')
THEN DebitAmt-CreditAmt ELSE 0 END) < 0 THEN (SUM (CASE WHEN COA_T.AccType in ('Cash & Cash Equivalents ','Marketable Securities','Accounts Receivable','Inventories','Prepaid Expenses','Fixed Asset','Intangible Asset','Investments','Other Non-current Assets','Accounts Payable','Accrued Expenses','Short-term Loans','Current Portion of Long-term Debt','Income Taxes Payable','Line of Credit','Term Loan','Capital','Current Year Earnings','Retained Earnings','Dividends','Share Capital','Paid in Capital','Open Balance','Sales Revenue','Operating Expenses','Administrative expenses') and COA_T.AccTransCate in ('BS','PL') and COA_T.AccTransSubCate in ('ASS','LBT', 'EQU', 'REV', 'EXP')
THEN DebitAmt-CreditAmt end )) ELSE 0 END AS [Credit]
FROM COA_T JOIN Trans_T ON COA_T.AccName = Trans_T.AccName
WHERE COA_T.AccType in ('Cash & Cash Equivalents ','Marketable Securities','Accounts Receivable','Inventories','Prepaid Expenses','Fixed Asset','Intangible Asset','Investments','Other Non-current Assets','Accounts Payable','Accrued Expenses','Short-term Loans','Current Portion of Long-term Debt','Income Taxes Payable','Line of Credit','Term Loan','Capital','Current Year Earnings','Retained Earnings','Dividends','Share Capital','Paid in Capital','Open Balance','Sales Revenue','Operating Expenses','Administrative expenses')and COA_T.AccTransCate in ('BS','PL') and COA_T.AccTransSubCate in ('ASS','LBT', 'EQU', 'REV', 'EXP')
GROUP BY COA_T.AccCode,COA_T.AccName ORDER BY COA_T.AccCode
END