If the Libraries do not have access to the titles you need, check free platforms like the Internet Archive or Open Culture or use paid services such as Hulu, YouTube, Netflix, Amazon, Criterion Channel, or Great Courses Plus. Keep in mind that you cannot screen films from these platforms, even for educational purposes.  

The reason films from these platforms cannot be shown in class and the Libraries cannot subscribe to them is because of their Terms of Service, which limit use to personal, private, and/or non-commercial use, and the individual user agrees not to stream content publicly e.g. §6(b) of Netflix Terms of Use). Netflix does have a list of films that grant a one-time, "educational license" to screen in classrooms. These films are documentaries which have been deemed "culturally significant" by Netflix and are the only films which can be screened without prior permission. 

“Cartoon Mobile Tablet Streaming a Video Online" by Vectortoons is licensed under CC BY-SA 4.0.