ZNY Controller witnessed loss of separation when a military flight requested breakup; multiple destination changes; and then declared an emergency; resulting in an operational error. Limited airspace and distractions listed as casual factors.

Narrative

2 sets of military flights were flying northbound -- both sets were nonstandard and in the process of aerial refueling. Both flights were handed off to the next sector. The flights decided they wanted to split up and Flight X would return to ZZZ -- back through our airspace; and Flight Y would continue northbound. So we took radar contact on Flight Y and in the meantime Flight X decided he wanted to go back to ZZZ so we took the handoff on that aircraft as well. In the meantime; Aircraft Y was a departure out of New York going overseas and was climbed to FL230. Again the military flights had a request that Flight X now wanted to change his destination; once again; to ZZZ1. The D-position during all this was putting in the many amendments on the flights and looking up routings for the destination changes when Flight Y requested to descend lower. The Radar Controller; I believe; because she was so frazzled with all the military flight changes; meant to descend the Flight X to FL240 because he/she did put that in the data block but instead climbed the aircraft to FL240 which was still showing FL230 in the data block. Now Flight Y declares an emergency and says he/she is proceeding direct ZZZ -- right through all the New York departures (in the direction of ZZZ2) and descending from FL250 to 10;000 FT. These flights and military flights always come through with many requests and the 2 sectors they fly through are just too small and too busy for break-ups; changes in destinations; etc. There is just not enough time to issue these clearances; put them in the computer and hand them off; not to mention keep the sectors under control with all the other airplanes. The military aircraft cause problems almost every time!