How can I make an object with curved surface touch sensitive with Arduino?
Your on the right track with capacitive touch, however you can make it all internal to the ball, as the touch sensing for this method works through most plastics, I would recommend using copper tape on the inside as the adhesive and plyability make it much easier to work with, you will need a big copper area e.g. 3cm x 3cm, and spaced about 1cm away, a line with your arduino ground, you will probably want a few of these around the device, 

you charge this capacitor up with the arduino pin pullup, turn off the pull up, then take an ADC reading of that pin, the ADC has a small capacitor inside that it uses to sample the analog voltage, in this situation it acts as a charge divider, so the sensor capacitor discharges a little and the ADC capacitor charges up a lot, 

This voltage reflects the dielectric of the material across the sensor, now water, water is a crazy good dielectric, 80 times better than air, and about 8-20 times better than most common materials or rocks, and humans, humans are made of water, so the persons hand is over the sensor, the capacitance of the sensor is higher, so the ADC voltage is higher, and suddenly you can tell when a person is there,

Main quirk and why touchscreens don't work well in the rain is its hard to tell a persons finger apart from a rain drop, so if it rolls through a puddle or gets water sprayed on it, it will give false triggers.