Mix 1/2 cup of laundry detergent with 1/2 cup of fabric softener. You can choose the detergent that best meets your needs. You can use a free and clear detergent if you have babies, or allergies or a pet with allergies. You can use a cold water formula if your carpet cleaner is not heated. Whatever you choose, make sure it does not have bleaching agents. You may use a color safe bleach however, like Clorox 2. You can use any fabric softener but you may want to coordinate the fragrances with your detergent.
The most important thing to remember is that the manufacturer will never approve this method, as the owners' manual demands users purchase Bissell's