I have a friend, Italian living in Split who passionately loves picigin. There are many things he did in his life which can make him a genuine Splićanin (locally for a person who lives or originates in Split), but very few of those things can measure with a fact that he has his own picigin ball.
You should know what picigin if arriving to Split is, it's probably the only beach fun protected by law as a part of cultural heritage. Some are annoyed for such attention, some will hate that cameras are often around to spoil their fun. However, whatever one might think, a little ball is in the centre of everything about picigin.
In more than a few occasions I've been asked by some tourists - while I was desperately trying to run and jump in Bačvice beach shallow waters - where they might buy this magic piece of rubber. Disappointment was serious after they would realize that DIY is the only way. There are, of course, people at Bačvice who are making them, just ask for the legend among them, Drago Krpetić. He even published instructions online, unfortunately only in Croatian. However, nothing can beat your own product, no matter how imperfect.
So, if you are interested, it goes something like this. Get somewhere a well worn-out tennis ball. Take a knife, or a razor, and slightly cut a joint of the canvas. Take some pliers, and firmly pull the canvas, it should go off. It was easy part.
Find some rough wall, and scratch all the glue remains. After that, sand your ball, first with rough, and then with smooth sanding paper. Drago says that ideal measure is to decrease a rubber thickness in half, but be careful, it can easily break. To be sure that you will sand it equally, and get a perfect shape, coloured part of the ball with a pen or a marker, sand it until paint disappear, and then go to another part. Never use sanding machine, it's hard to control it.
Now you are ready. Show up at Bačvice beach holding your product. You will have all the rights to show off.