1) Online students
Have you ever considered offering online lessons to students from different areas? If you do, you will be able to open up earlier hours when kids in your area are still in school.
2) Morning lessons
Try to get all of your adult and homeschooled students in the morning times to leave open more times for your other students. If you are struggling to get more adult and homeschooled students, you can post about your business in local groups and homeschooling groups in your area.
3) Redoing your schedule
Maybe you have enough hours but not all of your student's schedules fit with your current schedule. Try doing a complete makeover of your schedule. Ask students what their best times are for lessons and completely rearrange your schedule every six months so that your parents are getting the best times that they need.
The easiest way to have parents tell you what they want is to print off your hours and have parents rate their top 5 times that they prefer. You can also have them cross out any times that do not work for their schedule.
4) Irregular times
When I say "irregular times" I mean times like 3:45 or 6:15. Many schools get out at irregular times as well so you can start your teaching day right after schools get out. For example, you may be able to start at 2:45 instead of 3:00 and you would be able to have 15 minutes more of your time every day.
5) Group classes
You can try starting off your newest students in groups of 3-6 so that students can learn the basics of music. If they are enjoying music, they can continue with private lessons when new spots open up. Allowing for group classes will also increase your hourly income and gives opportunity for ensemble performances.
6) Buddy sessions
You can have two lessons overlap so that students are sharing part of their time with another student. Here are a couple of options that you can do:
30 minute buddy lesson - 20 min solo and 10 min buddy time
45 minute buddy lesson - 25 min solo and 20 min buddy time
60 minute buddy lesson - 40 min solo and 20 min buddy time
You can implement this in your studio to get your students practicing with evenly leveled duets, improvisation duets, or music games with each other.