Sensor options to detect ball
How about modulated IR LEDs and remote control IR receivers?  Mount IR LEDs in black plastic tubes along one short side and the receivers on the other side, also in dark tubes.  The LED tubes should be pointed straight down the detector tubes.  Mount enough of them with even spacing so that any ball passing through will pass a shadow over at least one sensor, preferably at least 2 sensors.  For a 25 cm ball in a 50 cm opening, 2 sets should be enough, spaced 12cm from each side.  If the ball goes through the hole, it is guaranteed to break at least 1 beam.  

Then, modulat the LEDs at the frequency the detector is looking for.  I think it's going to be around 30 or 40 kHz.  You can use a 555 timer with a decent transistor to drive the LEDs.  Then all you need to do is AND or OR the outputs of the detectors together to get your 'score' signal, depending on the output logic polarity of the detectors.  

The reason I suggest IR remote control detectors is becuase they have two very useful filters to get rid of interference.  First, they are generally encapsulated in plastic that blocks everything but the IR wavelength of the LEDs, eliminating a lot of background light.  Second, they have a narrow bandpass filter and peak detector that is only sensitive to a narrow band of modulation frequencies, so even if there is a lot of e.g. sunlight shining on the sensor, it should still be able to extract the signal from the emitters.  

Edit: Here are all of the IR remote receiver sensors from Digikey.  I highly recommend using a bunch of these instead of bare photodiodes or phototransistors because of their built-in bandpass filters:

http://www.digikey.com/product-search/en/sensors-transducers/optical-sensors-photo-detectors-remote-receiver/1967024