I don't believe it was ever stated what language she was teaching, but it's fun to speculate!
My pick would be Draylaxian. In 2151, there wouldn't be that many species humanity had come in contact with, and certainly very few that are in regular enough contact to warrant a language course being set up. Except for a few visitors via Vulcan programs such as the Interspecies Medical Exchange, it was probably the Earth Cargo Service that had the greatest amount of alien contact. Denobulan doesn't seem to feature those trilling sounds, and as you say, it doesn't sound very Vulcan either.
So my guess is Draylaxian, since the ECS set up a regular trade route with them.