Bill figured out how to keep his daughter entertained (but engaged) while he watched the game:
My son Griffin (2) is crazy about football – almost every shirt he owns has a football on it – but my daughter Erin (4) never showed much interest in sports and would sometimes complain that she wanted to watch "her" shows while Daddy was watching a game.
One day after a penalty on the field I said, "Erin, did you see that zebra?" The two of them looked at the TV and screamed excitedly when the official trotted onto the screen in his black-and-white striped shirt. Now every time I watch a game, they happily go on "zebra watch".
I came up with it at the beginning of the pro football season, but this approach should work for most sports; baseball and soccer are the only exceptions I can think of.
I, too, watched a lot of TV football and tennis with my Dad when I was a kid. I'm not a sports fan (never was) but I still look back on those times with a lot of warmth.
More: Hacks for sports-loving (or -playing) families