Conga Orchestrate gives you the ability to disable custom object triggers created through the setup wizard with the following steps.
Adding a checkbox field to the Conga Orchestrate Settings custom setting called 'Disable_{Namespace}_{Object_Name}_Trigger' allows custom object triggers to be disabled like standard object triggers.
A single underscore between the namespace and the object name is important if there is a namespace. The case does not matter.
When the checkbox is selected, the trigger is disabled and will not run.