It depended on what R/W's LGA was using. If they were departing to the west, it's a no go. That was the only time I was denied.
Looking at the TAC, it looks like 126.05 was the freq I made the request on. It doesn't ring a bell, but it was >2 years ago that I was up there. I would call them up 1-2 miles south of Governor's Island with the request "I'd like to go up the east river and over central park to the hudson @ 1500'". They'd either say, "Cessna XXX cleared into Class B, climb and maintain 1,500" or "Remain clear of Class B". Pretty easy.
~wheelsup