As with audio-visual material, music recordings may only be played in lectures and tutorials if you have the relevant permission to do so, or if it is covered under a licence. This applies whether they were purchased, borrowed from the library or hired.
Unfortunately, as a private university, TUA is not able to take advantage of the exception offered to most educational institutions under section 28 of the Copyright Act, which deems performances ‘in class’ in the course of educational instruction not to be a performance in public, so long as the audience is limited to those taking part in the instruction (i.e. University staff and students only - no parents or other guests). This exception is only available to not-for-profit institutions.
There is no general licence or copyright exemption that permits you to make a copy of music recordings without permission from the copyright owner, even for educational purposes.
If permission is obtained to use music recordings on BlackBoard/Canvas, it should be lodged with the University Copyright Officer for recordkeeping, by email to firstname.lastname@example.org.