1. Beat butter, rum, and extracts in a bowl until blended. Gradually add about 1 1/2 cups of the confectioners' sugar, continuing to beat until fluffy. Beat in egg yolks, one at a time.
2. Blend instant coffee and cocoa in a small cup; add the boiling water and stir until thoroughly mixed; cool. Beat into the butter mixture with the remaining 1/2 cup confectioners' sugar. Chill until ready to use. Allow to come to room temperature; beat, if necessary, to spreading consistency.