Isn't the probability of c and d half that of a and b? If BG is the case, there's 100% chance he's talking about the first child. If BB is the case, there's a 50% chance he's talking about the first one, and a 50% chance he's talking about the second one.

    BG, giving the first - 1/3
    GB, giving the second - 1/3
    BB, giving the first - 1/6
    BB, giving the second - 1/6

[Edit] You're right. Tables can be a bad way of thinking about it, because you have to make sure each option has an equal probability for them to work. This is okay when you have a single variable (like in the original post), but gets tricky when you introduce a new variable (as you did: is the father thinking about the first or second). Once you get past one variable, trees are probably a better but still simple representation.