N90 CTLR SEQUENCING TFC FOR VISUAL APCHS FOR LGA MISSPOKE A CLRNC THAT RESULTED IN A CONFLICT BTWN 2 ARR ACFT.

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I WAS ASSIGNED A RADAR POS THAT WAS VERY BUSY. AFTER WORKING THE POSITION FOR 1 1/2 HRS; I WAS ASSIGNED A 30 MIN BREAK AND THEN I WAS ASSIGNED ANOTHER VERY BUSY RADAR POS. AFTER ANOTHER 1 1/2 HRS; THE LOSS OF SEPARATION OCCURRED. AT THE TIME OF THE INCIDENT; I WAS RESPONSIBLE FOR 9 ACFT AND WAS VECTORING THEM TO A DOWNWIND LEG OF THE LGA FINAL APCH. STANDARD PRACTICE DURING VMC OF THIS PARTICULAR RWY SETUP IS TO SEND THE ACFT VISUALLY TO EITHER THE VERRAZANO BRIDGE OR THE STATUE OF LIBERTY AND INSTRUCT THEM TO THEN FOLLOW THE HUDSON RIVER NEBOUND. AT THE TIME OF THE INCIDENT; 4 OF THE AIRPLANES UNDER MY CTL WERE FOLLOWING THE RIVER WHEN I NOTICED THE SECOND IN THE LINE REDUCE THEIR SPD. I ASKED THAT ACFT TO INCREASE THEIR SPD; AND THEN TO MAINTAIN SEPARATION. I SLOWED AND VECTORED BOTH OF THE TRAILING ACFT TO A NWBOUND HDG. THE FIRST OF THE 2 TRAILING ACFT; AN MD80; WAS APCHING ANOTHER CTLR'S AIRSPACE; SO I TURNED THEM BACK TO A NEBOUND HDG TO KEEP THEM IN MY AIRSPACE AND I ISSUED THEM A DSCNT TO 3000 FT. THE SECOND ACFT; AN A320; WAS INSTRUCTED TO GO TO THE STATUE OF LIBERTY AND FOLLOW THE RIVER. I THEN WENT BACK TO THE MD80 AND MEANING TO TELL THEM 'WHEN OVER THE RIVER FOLLOW IT NBOUND' I TOLD THEM 'OVERFLY THE STATUE OF LIBERTY AND FOLLOW THE RIVER NBOUND.' SINCE THE MD80 WAS ALREADY N OF THE STATUE; THEIR TURN TO GO BACK TO IT AND FOLLOW THE RIVER PUT THEM IN CONFLICT WITH THE A320. THIS SEQUENCE OF EVENTS HAPPENED QUICKLY ENOUGH THAT THE MD80 HAD NOT STARTED THEIR DSCNT. DURING THIS INCIDENT; I WAS ALSO PERFORMING A MANUAL RADAR HDOF FROM ZDC. MORE EFFECTIVE TFC MGMNT AND LESS TIME ON BUSY POSITIONS WOULD HAVE AVOIDED THIS SIT. SUPPLEMENTAL INFO FROM ACN 666662: WE WERE FLYING UP THE HUDSON RIVER VISUALLY INBOUND TO LGA. APCH CTL ISSUED US A BRIEF TURN TO THE W AND THEN CLRED US TO TURN BACK TOWARDS THE RIVER TO FOLLOW IT VISUALLY NBOUND AGAIN. SHORTLY THEREAFTER; WE NOTICED A CONVERGING ACFT ON TCAS AT OUR 10 O'CLOCK POS AT OUR ALT. WE CONFIRMED THE TARGET VISUALLY AND SHORTLY THEREAFTER RECEIVED A CLB RA ALERT ON TCAS. WE INITIATED A CLB AND TURNED AWAY FROM THE TARGET WHILE MAINTAINING VISUAL CONTACT AT ALL TIMES. THE APCH CTLR INDICATED THAT HE HAD MADE AN ERROR AND APOLOGIZED. THIS CTLR WAS VERY BUSY ISSUING VECTORS TO NUMEROUS ACFT DURING THIS EVENT. WE WERE THEN RE-CLRED BACK UP THE RIVER AGAIN FOR AN UNEVENTFUL VISUAL APCH TO RWY 22 AT LGA.