How do I create an apple ID for a child for itunes if I don't have an ipad or mac?

Does the child you want to create the account for have an Apple device? If the child is less than 13 years old, you will need to set up Family Sharing. It can be done using one device, but it is a bit more difficult using only one device. On the device, sign into iCloud with your Apple ID and set up Family Sharing. Create the child's ID. Sign out of your ID and sign in with the child's ID. Swap iCloud sign in as required.

Family Sharing.         

Family Sharing - Set up.       

Family Sharing and Apple ID for your child

Set up - your child’s iPhone, iPad, or iPod touch