The order of liabilities is not as structured as that of assets. Current liabilities will be listed first, but the order within current liabilities will vary from company to company.
Some companies will list the current liabilities in this order: 1) short-term notes or loans payable, 2) current portions of long-term debt, 3) accounts payable, 4) payroll related liabilities, 5) other accrued expenses, and 6) income taxes payable. Other companies will list its accounts payable ahead of its short-term debt.
After the current liabilities are listed, the long-term or noncurrent liabilities will be listed. This might include long-term debt, bonds payable, and deferred income taxes.
In short, I would arrange the chart of accounts in the order that the accounts will appear on the balance sheet and income statement.