Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Great Falls to Riviera Maya as you normally would.
Due to multiple factors, expect to potentially pay more when booking in June. For low rates, October can be a great choice for travel to Riviera Maya. Flights to Riviera Maya from Great Falls in October are about $813 on average during October, but can be found for as low as $632.