Can I apply through a travel agency in Fukuoka, Japan as a foreigner?

I live in Miyazaki, Japan. I'm planning a trip to China in August. The nearest Chinese embassy is in Fukuoka, about three hours away. I also work every day and taking time off is hard. How long before my trip do I need to apply for the entry permit? Also, if it's possible, would it be easier to apply through a travel agency?