One way to get from Avalon Airport to Melbourne CBD is by Avalon City Express. It's 24 AUD one way or 46 AUD roundtrip. I was wondering whether there are any other transportation options that are cheaper?
Nope. Other than the Sky Bus (City Express) there's no other means of getting in outside of a taxi.
Avalon Airport (AVV IATA) is a mainly domestic airport 55 km south-west of Melbourne in Lara, near Geelong. Although much further than Melbourne Airport, fares from Avalon are sometimes considerably cheaper. The terminals are generally very simple, with just an ATM, car hire desks and baggage carousels. Other facilities include a cafe, bar and a video arcade room. There are several flights in and out of Avalon each day, with many domestic operated by lower-cost airline Jetstar (which also flies to Melbourne Airport) and an AirAsiaX flight to Kuala Lumpur.
SkyBus operates a coach shuttle to Southern Cross Station in Melbourne's City Centre via the outer western suburb of Werribee, meeting every flight arrival and departure. The transfer costs $22 one-way for an adult, and $10 for a child (4-14 years). Other than the coach, there is no public transport; Lara Station is 8 km from the terminal, meaning one could ride a bike on the road to/from the airport or catch a taxi, which would cost about $15 to the station. A taxi to the city from the airport could cost upwards of $100.
You could try to hitchhike, but other than that, you're really stuck with the bus.