Place ground coffee in coffee filter and add cold water to coffee maker and brew to make 1/2 cups. Combine brewed coffee and 2 Tbsp jahlua in a shallow dish, cool. Combine cheeses in a large bowl.
Beat with mixer at high speed till smooth. Add 2 tbsp Kahlua and sugars, beat until well blended.
Split ladyfingers in half lengthwise, quickly dip 24 fnger halves, flat sides down, into bottom of 8" sq pan (halves will slightly overlap)spread half the cheese mixture over ladyfingers.
sprinkle with 1 tsp cocoa. Repeat procedure with remaining ladyfinger halves, coffee mixture, cheese mixture and 1 tsp cocoa. Place a toothpick in each corner of dish and 1 in center of triamisu to prevent plactic wrap from sticking)cover with plastic and chill for 2 hours.