Niko, Not sure where you are but I have exactly the right chemicals but it would not be possible to post them, I am in Lancashire.
However a crude form of rust browning can be achieved with salt water, it will probably require several applications and clean off with de-greased wire wool after each coat until the desired colour is obtained. Lastly apply soda water solution to kill the rusting. [washing soda] The colour will depend on the type of steel/iron the ball is made of, steel does not brown easily, iron does.
Regards John