Is this the only day you will use public transport services? We would have to know your entire itinerary in order to suggest a travel pass or other sort of reduced tickets. It is advisable to complete the trip planning first and, as the last step, to decide on the ticket.
As a general saying, if your overall ticket cost for the cost per person exceeds CHF 240, then the Swiss Half Fare Card is a great deal. It comes with the complimentary Swiss Family Card, with it, your 6 years old travels for free with you. Alternatively, there is the Junior Card for CHF 30, valid 1 year, with it, your 6 years old travels also for free when travelling with you.
For this single trip from Geneva Airport to Montreux:
- 2 full fare point-to tickets (CHF 35)
- 1 half fare point-to-point ticket (will be issued automatically when you enter the date of birth) (CHF 17.50)
- The 3 year old does not need a ticket at all (children 6-15.99 years of age)
The suggested tickets are valid on any train/connection for that day.