A couple of options, which are limited because you're renting.
1) Draw your curtains closed to keep the sun out
2) Air movement really helps! Create a draft by opening doors or windows in the North and south sides of the house. If you don't have them, put some catches on the doors so they don't slam shut with the draft.
3) You might be able to install a ventilator in the attic space that removes the warm air and helps to reduce heat gain from above into your house.
This is a pretty good video. Didn't know about the other problems mentioned.
4) If 3 isn't an option consider insulate the ceiling (which is good for both summer and winter) - your landlord may pay for it, but if not it may pay for itself in savings to you if you're planning on staying long enough. If it's already insulated then you may benefit by adding more.
This will prevent excess heat entering the home from above (or leaving in winter). This heat gain is especially bad on homes with an iron roof.
For people who own their own homes that have heating/cooling issues.
Trees that shade in summer and drop their leaves in winter help enormously.
As do plants that cover housing like ivy. They keep the heat off of the building and insulate it. Not everyone wants ivy growing on their houses though.
Another option is to install awnings which fold out for summer use and provide shade from the high sun. It's a manual and in my opinion less attractive solution to using plants.
Cool the ceiling or attic space with a ventilator. This removes the hot air and helps prevent it heating up your home. You can get solar ones or passive ones.