To pay super from MYOB you need to process the super payments through payroll. This means to pay super for a contractor you'll need to set up the contractor as an employee to pay their super. Just manually add them as an employee and enter their super details.
If you pay the contractor via invoices they send you, you will also need to set the contractor up as a supplier so you can pay their bills like any other. Then when you process your payroll to pay super for the contractor, only enter the super amount into their pay (and no other amounts). You can then declare the pay to the ATO as part of your STP reporting.
