You would need to put your students through a separate website and "paywall." The webiste allows yo to showcase your learning materials and perhaps show free samples. The paywall allows you to register the students, collect the fees, provide links to paid content, and provide access to other services and products you might want to offer. One payment is collected, the links behind the paywall could theoretically go to screencast.com as the streaming service. I have not tested this, but it just makes sense.
Look for shopping cart or paywall services available on the web. Many ISPs have components to build websites and paywall services.