Controller described a loss of separation event when approving several turns to land on other than the active runway at nearby military airport; complicated by weather and airspace constraints.

Narrative

Air Carrier X was inbound. [I] advised the aircraft of the weather that was near the final approach course for Runway XX. As aircraft neared; he had asked if Runway YY was available at [the same airport]. It was not a problem; as I saw no weather between him and [his destination]. As he was getting closer he asked for a left 360 degree turn to get to final for Runway YY. I was unable to do that because of restricted airspace. He made a right 360 degree turn and then was issued a Visual Approach clearance. At this time an aircraft departed [a nearby airport] to head northwest bound climbing to 8;000 FT. Controller advised me that the aircraft wanted to do another 360 degree turn to the right to land Runway YY and I approved the maneuver. What happened after that was the aircraft asked to help him to a six mile base leg for Runway YY and the Controller advised that they could not help him with that as that would take him back out into class C airspace. I was then advised that the aircraft was coming back to me and when he was switched to me he was heading southbound. I turned the other aircraft and asked that he expedite his climb through 3;000 FT. When I was finally able to talk to the aircraft; I issued a hard left turn to vector him for the ILS to Runway XX. The turns did not work and they passed 1.5 miles laterally and 800 FT vertically.