You can use a paper filter instead of a permanent coffee filter.
Paper coffee filters are actually better than permanent coffee filters as they help to keep the grinds from dripping into the coffee and help the coffee brew better and creates a more flavorful cup of coffee.
Paper coffee filters are not that expensive and I prefer myself to use paper coffee filters over permanent coffee filters.
It's also better to simply throw the coffee grounds and paper coffee filter out instead of having to wash the permanent coffee filter.
Coffee shops use paper coffee filters as well instead of permanent coffee filters as it gives the coffee a better taste.
If you run out of coffee filters and need to make coffee you can also use a few paper towels in place of the paper coffee filter.