In certain cases where you have repaid some installments of a previous student loan independently, you would be given the authority of branching away the Co-borrower. This is known as Co-Borrower Release and by doing so, you ensure that the loan repayment is entirely yours. This also puts you in a position where you are not hit by the Credit History of your Co-Borrower. Both of you are separate entities speaking from the loan perspective and you would hence need to take charge of repaying your loan off.
"Insurance" organizations, who collect premiums for providing either life or property/casualty coverage, created their own types of loan agreements. "Banks" and "Insurance" organizations loan agreements and documentation standards evolved from their individual cultures and were governed by policies that somehow addressed each organizations liabilities (In the case of "banks," the liquidity needs of their depositors; in the case of insurance organizations, the liquidity needs associated with their expected "claims" payments).
Whatever is agreed regarding applicable penalties for late or inability to comply should not only be discussed but also defined. Payment deadlines also should be set and included in the loan agreement as well. In order to effectively carry out the terms in the agreement, it is but proper to include the contact information of both the lender and debtor should the need arise to call them out.
Start your research today and trust me, you will find one or the other lender who will be able to give you a loan without your co-borrower. Please note that having or not having a co-borrower for your loan is subject to the credit history of your co-borrower. If he has a good credit history, you would not mind getting him on-board for signing the loan agreement. Think twice if it is otherwise.