The short story: if you are going to be gone for a week to ten days, and your fish are healthy and well fed, just let them fast while you are away. They will be fine, the water will stay cleaner, and you will avoid having other people try to second guess your care instructions.

If you can lower the temperature towards 60 degrees Fahrenheit or cooler (don’t drop more than 2 degrees per day), you can leave adult fish unfed for at least a month.

The problem with alternatives is that non-goldfish people cannot stand to "underfeed" goldfish the way we have spent years learning to do. I have heard horror story after horror story of well-meaning friends dumping a week’s worth of food into the tank on the first day, fouling the water and leading to sick or dead goldfish by the time the owner returns. If you have to have someone come in and do care while you are away, you must idiot-proof the process. Pre-measure the food into individual serving containers with strict instructions on when to feed. I would suggest a half feeding every other day as a good choice for up to 6 weeks. Even if you have an experienced goldfish person doing the care, do this. It will free them of guilt if something goes wrong, since they were following "your system".

One additional possibility, if your filtration can handle it, is to provide greenery for your fish to eat. Aquatic plants are good and even romaine lettuce leaves will be okay for a week or two if submerged. The fish can nibble on this as they get hungry. I would suggest testing this method out, though, before depending on it. What can happen is that the fish suddenly discover that they love romaine lettuce, reduce all of it to puree in an hour or two and totally clog the filter with vegetable matter. This situation is, of course, much worse than just letting them go hungry. Which brings us back to the first point.