Not sure if it's still there but we've watched a few games in the pub by Chichester station, had a massive big screen and loads of TV's scattered about. Might be worth a try.
You'll be very luck to find anywhere decent in Rustington or Littlehampton that actually show live football, perhaps the following:
Littlehampton
The Crown
The White Hart
Rustington
The Dragon
Rustington Football Club