According to the MTA, there will be Roosevelt Island F Train service
to and from Manhattan this weekend. Also, there will be E Train Roosevelt Island train service to and from Manhattan as well:
E Trains run via the F in both directions between W 4 St and 21 St-Queensbridge
But, there will be no Roosevelt Island Tram elevator or chair lift working this weekend. 
Image of Out Of Service Tram Passenger Elevator and ADA Red Lift From May 29 2013 According to the Roosevelt Island Operating Corp ( RIOC ):
Due to the ongoing Tram platform renovation project, the Tram Elevator and Chairlift on the Manhattan Platform will be temporarily out of service on Saturday, September 23rd and Sunday, September 24th. During this time, RIOCs Transportation Department will provide shuttle bus service to Manhattan and R.I. departing from the Southwest side of 2nd Ave between 58th & 59th Street. Shuttles will leave on the hour from Roosevelt Island and on the half hour from Manhattan beginning at 11 AM. The last shuttle bus will depart from Manhattan at 7:30 PM.
Tram Elevator and Chairlift access on the Manhattan Platform will resume on Monday, September 25th.
We apologize for the inconvenience.
During the September 7 RIOC Board of Directors meeting (full video web cast of meeting here) , RIOC President Susan Rosenthal reported on the Tram elevator and chair lift being out of service
this weekend.