Keith wants to bring a total of 96 cupcakes to the bake sale, and he has already made 36 cupcakes. Thus, the number of cupcakes he still needs to make is:
\[ 96 - 36 = 60 \text{ cupcakes} \]
The recipe calls for 8 tablespoons of butter for a batch of 12 cupcakes. To find out how much butter is needed for the 60 cupcakes, we first determine how many batches of 12 cupcakes are in 60:
\[ \frac{60}{12} = 5 \text{ batches} \]
Since each batch requires 8 tablespoons of butter, the total amount of butter needed for 5 batches is:
\[ 5 \times 8 = 40 \text{ tablespoons} \]
Now, to convert tablespoons to cups, we use the fact that there are 16 tablespoons in 1 cup:
\[ \frac{40 \text{ tablespoons}}{16 \text{ tablespoons/cup}} = \frac{40}{16} = \frac{5}{2} \text{ cups} \]
Thus, the amount of butter Keith will use for the rest of his cupcakes is:
\[ \boxed{\frac{5}{2}} \] or 2.5 cups.