A gentle workout on a sunny beach or in a park is much more enjoyable than sweating away in a gym, and it doubles as a social occasion, allowing people to chat and make friends. You could even organise jogging and cycling excursions, offering participants the opportunity to explore the local countryside.
This idea is perfect for the summer months. Contact existing exercise classes and discuss your proposition - they may be interested in employing your services as an extension of their class.
Alternatively, go it alone. Advertise in shop windows, sports clubs, the local paper, tourist attractions and accommodation. Either yourself or a friend could hand out flyers to passing tourists and locals - make sure the times and dates of your classes is clearly printed on it. An attractive sign is always a good idea too.