Accountability needs to be an ingredient. Students need to realize that they have responsibility for the activities with the computer. This can come about through assignments done at regularly scheduled time with the music classroom computer or accessible computers elsewhere. If your school has a media center, computers might be available there for student use on music assignments. If a computer lab is available at your music time or at other times during the day, this could be an answer.
Every school has different facilities.
Check out where the computers are in your situation. Check out the possibility of your students' using those computers. Find a way to have the software you want students to use on those computers. It might be possible to use a program that is on the Web for your assignments. Then you just need a computer or computers that have Web access.