Brew 1½ cups coffee in drip coffee maker. Combine the brewed coffee and 2 tablespoons Kahlúa in a shallow dish and cool.
Combine cheeses in a large bowl. Beat on high speed of a mixer until smooth. Add sugars and 2 tablespoons Kahlúa and beat until well blended.
Split ladyfingers in half lengthwise.
Quickly dip 24 ladyfinger halves, flat sides down, into coffee mixture; place dipped sides down, in the bottom of an 8-inch square baking dish, slightly overlapping ladyfinger halves.
Spread half of cheese mixture over ladyfingers; sprinkle with 1 teaspoon cocoa. Repeat procedure with remaining ladyfinger halves, coffee mixture, cheese mixture and 1 teaspoon of cocoa.
Place 1 toothpick in each corner and 1 in the center of tiramisu (to prevent plastic wrap from sticking to cheese mixture). Cover with plastic wrap. Chill 2 hours.
