I have a background music system at a community center I am about to install and would like to restrict access to the Sonos system. Would it be possible to utilize the existing Ubiquiti UniFi access points to create a separate guest network/ SSID that would only allow users to access Sonos through that wifi connection even though both networks are supported by the same router?

Should be easy enough for you to test. If the Sonos player is wifi you can set it up to be on the specified wifi network in the advanced wireless setup portion of the Sonos app. You have to set it up while hardwired, configure it for the wifi, then disconnect it from the hard wire. I just tested mine on wifi only...Sonos was accessible via the wifi it was configured with but not accessible via another wifi network I have running on the same LAN.

VLAN

Yes create a separate VLAN for the Sonos and then create a new Wireless network with that VLAN. You may have to create it as a corporate network and then manually create rules to block access to the main network. This is because I believe a guest network automatically creates rules where 2 devices on that network cannot connect to each other only access through the gateway for internet but I could be wrong.