Accomodation and animals have been a problem in Melbourne for a long time. You could write out a comprehensive case detailing the low risk and the support of the neighbours, and any other pro bee information you can find, but some people are very stubborn. Sometimes though, the effort of a well researched argument will pay off. Could you get some advice from the rental tribunal also or your estate agent? Also, find out if there are any council restrictions where you are.
When I was having trouble getting bees into town here, the DPI said they would write to the council if necessary. However, your landlord can place any such restrictions he wants to on the property.
Unfortunately, the easy going disposition of many australians is mostly a thing of the past, and a change in attitude is going to involve educating the kids while they are still young enough to enjoy nature.