HCF coordinator described operational error event involving two trainees on both arrival positions; the reporter noting neither of the trainee's knew what to say and both instructors failed to provide guidance; adding he/she should have intervened sooner and been more forceful about the resolving the developing conflict.

Narrative

Training on both RADAR arrival positions; H and V. Aircraft Y being vectored by H trainee for visual approach to Runway 4R; handed off to V trainee approximately 5NM northeast of HNL. V trainee turns Aircraft Y to a 220 heading; downwind; and descends him to 060. Air Carrier X departs Runway 8R; turning to a 155 heading; climbing to 050. I tell V trainee we're stopping at 050. V trainer and trainee say they're stopping Aircraft Y at 060. Their courses cross approximately 5 NM South-Southeast of HNL. V trainee then descends Aircraft Y to 015; then goes back and stops him at 030 for inbound traffic. Meanwhile; H trainee turns Air Carrier X to a 260 heading. V trainer sees Air Carrier X turning and asks what he's doing. I tell him he's turning to a 260 heading stopping at 050. V trainer stops Aircraft Y at 050. Aircraft Y asks for the altitude again and V trainer says turn right heading 300. V trainer then issues Aircraft Y a traffic alert and tells him again to turn right heading 300. Meanwhile; you hear a couple clicks on H frequency. You hear H trainee say ' Air Carrier X' twice; but give no instructions. H trainee gives traffic call to Air Carrier X and he reports Gulfstream in sight at which point H trainee tells Air Carrier X to maintain visual separation; however separation was already lost. After both aircraft are separated Air Carrier X uses the words 'traffic avoiding' or 'traffic avoidance' and advises heading 260 maintaining 050. Air Carrier X never stated that he was responding to a TCAS RA; however; he did climb to about 055 or 056 when H trainee was issuing traffic. Along with his wording of the 'traffic avoiding' and climb I believe he was responding to a TCAS-RA; but did not advise of it. Recommendation; H; W and V personnel were assuming each was doing something different. H was under the impression that V was going to keep Aircraft Y above Air Carrier X as he turned westbound. That is what I thought H was going to do as well; even though that was not a wise decision. Aircraft Y would get screwed due to having to fly a 20 mile downwind while Air Carrier X got out of the way as he flew westbound. V thought H was going to leave Air Carrier X on his initial departure heading of 155 and continue his climb after their courses had crossed; which is why he descended Aircraft Y when he did. I made mention that something had to be done with Air Carrier X; a turn or descent; something; but I was not forceful enough. The H trainee had no idea of what to do to ensure they did not hit. Separation was lost; there was nothing that could salvage that situation; however; after acknowledging that the situation was turning from bad to worse; the trainee couldn't say anything and was clearly shaken after the incident. I should have told him what to say since the H trainer didn't say anything. In the H trainee's defense; he did ask his trainer repeatedly what he should say. I should also have told V when Air Carrier X was given the 260 heading; but more importantly I should have noticed Aircraft Y descending and told the H trainee not to turn Air Carrier X; instead leave him on his 155 heading. In short; I should have told each person to wake up and pry these two airplanes apart; and been forceful about it; rather than waiting for each trainee and trainer to get it done.