There are several causes for a sulphur smell to occur in your water tank:
Sludge and soil contamination at the bottom of your tank
Poor aeration of the water tank causing anaerobic conditions.
If leaves, soil and debris are gathering in your gutter and flowing into the tank and dropping to the bottom, you might have to clean it out with a pool leaf scoop and clean the bottom of the water tank as best you can. Most folks chlorine bomb their tanks to kill off the bacteria in the tank and take the smell out as well, however this particular method is not good for your plants if you are using the water to irrigate them. Plus the chlorine in the water will damage the finish on your cars and furniture should you decide to use this water to clean them.
My best recommendation is to use an earth friendly rain tank purifier. There are currently dozens to choose from but our main objective is to look for the one that has the longest effect.
If the water in the tank is sealed and stays stagnant or is still for more than three months, that is enough time to produce anaerobic conditions. Simply topping up the tank with your garden hose and letting the tank overflow a bit is enough to introduce oxygen back in to the water. Thereby eliminating the possibility for poor oxygen conditions. Open the top of your water tank to let it air out is also a good strategy.
If the smell persists then perhaps it's time to use a more potent solution such as chlorine. However please be aware of the effect it could have on all your plants and other items that you may wish to use this water on. Chlorine eventually evaporates from water but it has to be exposed to the sun. Keeping your tank open to the air and letting sunlight in and topping up the water will speed up the process.
By my estimates chlorine will stay in the water for at least 30 to 40 days in a 5000 litre tank if left undisturbed. - redracer01
A first flush diverter on your system prevents sediment, bird droppings, spiders, insects, mosquito eggs and debris from entering the rainwater tank. When this organic matter breaks down within the tank, it creates the sulphur smell.