Cleint/trainer booking system for fitness multisite

Can anyone suggest a suitable plugin so that members can see the availability of particular trainers (these can be user levels of course) can be seen and a booking made on a multisite installation? The trainers will enter their availability (and the facility of course) and clients will be able to see this and book a session, taking any payment depending on the client membership level.

I have looked at the many calendar and booking plugins on the main WP system but either they don’t integrate with multisite or they are basically subscription services for hotels etc which is much more than I need (and more expensive too!).

Any clues deeply appreciated!