Unfortunately riding in Geneva is very expensive :/ At least compared to Australia. Let me know if you manage to find anywhere that won't break the bank! http://www.equinet.ch/de/index.php
often has horses for lease and part-lease.
I do have an extra voucher for 2 x 30 minutes private lessons in English or French at Centre Hippique de la Chaumaz, which I bought and am selling at half the usual price. I haven't ridden there yet myself, so can't say how good it is.